Distance against time graphs distance time. Constant speed distance time The gradient of this graph...
-
Upload
adam-mclaughlin -
Category
Documents
-
view
231 -
download
2
Transcript of Distance against time graphs distance time. Constant speed distance time The gradient of this graph...
![Page 1: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/1.jpg)
Distance against time graphs
distance
time
![Page 2: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/2.jpg)
Constant speed
distance
time
The gradient of this graph gives the speed
![Page 3: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/3.jpg)
Getting faster (accelerating)
distance
time
![Page 4: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/4.jpg)
A car accelerating from stop and then hitting a wall
distance
time
![Page 5: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/5.jpg)
Speed against time graphs
speed
time
![Page 6: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/6.jpg)
No movement
speed
time
![Page 7: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/7.jpg)
Constant speed
speed
time
![Page 8: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/8.jpg)
Getting faster? (accelerating)
speed
time
Constant acceleration
![Page 9: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/9.jpg)
Getting faster? (accelerating)
speed
time
a = v – u
t
(v= final speed, u = initial speed)
v
u
The gradient of this graph gives the acceleration
![Page 10: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/10.jpg)
Getting faster? (accelerating)
speed
time
The area under the graph gives the distance travelled
![Page 11: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/11.jpg)
A dog falling from a tall building (no air resistance)
speed
time
Area = height of building
![Page 12: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/12.jpg)
Acceleration/time graphs
acceleration
time
![Page 13: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/13.jpg)
Constant/uniform acceleration?
acceleration
time
![Page 14: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/14.jpg)
Note!
The area under an acceleration/time
graph gives the change in velocity
acceleration
time
![Page 15: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/15.jpg)
Displacement
• Displacement the distance moved in a stated direction (the distance and direction from the starting point). A VECTOR
![Page 16: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/16.jpg)
Displacement/time graphs
• Usually in 1 dimension (+ = forward and - = backwards)
Displacement/m
Time/s
![Page 17: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/17.jpg)
Velocity?
• Velocity is the rate of change of displacement. Also a VECTOR
![Page 18: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/18.jpg)
Velocity/time graphs
• Usually in 1 dimension (+ = forward and - = backwards)
velocity/m.s-1
Time/s
Ball being thrown into the air, gradient = constant = -9.81 m.s-2
![Page 19: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/19.jpg)
Acceleration?
• Acceleration is the rate of change of velocity. Also a VECTOR
![Page 20: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/20.jpg)
Acceleration/time graphs
• Usually in 1 dimension (+ = up and - = down)
accel/m.s-2
Time/s
Acceleration = constant = -9.81 m.s-2
![Page 21: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/21.jpg)
Average speed/velocity?
• Average speed/velocity is change in distance/displacement divided by time taken over a period of time.
![Page 22: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/22.jpg)
Instantaneous speed/velocity?
• Instantaneous speed/velocity is the change in distance/displacement divided by time at one particular time.
![Page 23: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/23.jpg)
The equations of motion
• The equations of motion can be used when an object is accelerating at a steady rate
• There are four equations relating five quantities
u initial velocity, v final velocity,
s displacement, a acceleration, t time
SUVAT equations
![Page 24: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/24.jpg)
The four equations1 This is a re-arrangement of
2 This says displacement = average velocity x time
3 With zero acceleration, this becomes displacement = velocity
x time
4 Useful when you don’t know the time
t)u+v(2
1=s
at+u=v
2at2
1+ut=s
as2+u=v 22
t
u-v=a
NOT in data book
![Page 25: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/25.jpg)
Beware!
• All quantities are vectors (except time!). These equations are normally done in one dimension, so a negative result means displacement/velocity/acceleration in the opposite direction.
![Page 26: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/26.jpg)
Example 1
Mr Blanchard is driving his car, when suddenly the engine stops working! If he is travelling at 10 ms-1 and his decceleration is 2 ms-2 how long will it take for the car to come to rest?
![Page 27: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/27.jpg)
Example 1
Mr Blanchard is driving his car, when suddenly the engine stops working! If he is travelling at 10 ms-1 and his decceleration is 2 ms-2 how long will it take for the car to come to rest?
What does the question tell us. Write it out.
![Page 28: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/28.jpg)
Example 1
Mr Blanchard is driving his car, when suddenly the engine stops working! If he is travelling at 10 ms-1 and his decceleration is 2 ms-2 how long will it take for the car to come to rest?
u = 10 ms-1
v = 0 ms-1
a = -2 ms-2
t = ? s
![Page 29: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/29.jpg)
Example 1
Mr Blanchard is driving his car, when suddenly the engine stops working! If he is travelling at 10 ms-1 and his decceleration is 2 ms-2 how long will it take for the car to come to rest?
u = 10 ms-1
v = 0 ms-1
a = -2 ms-2
t = ? s
Choose the equation that has these quantities in
v = u + at
![Page 30: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/30.jpg)
Example 1
Mr Blanchard is driving his car, when suddenly the engine stops working! If he is travelling at 10 ms-1 and his decceleration is 2 ms-2 how long will it take for the car to come to rest?
u = 10 ms-1 v = 0 ms-1 a = -2 ms-2 t = ? s
v = u + at
0 = 10 + -2t
2t = 10
t = 5 seconds
![Page 31: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/31.jpg)
Example 2
Jan steps into the road, 30 metres from where Mr Blanchard’s engine stops working. Mr Blanchard does not see Jan. Will the car stop in time to miss hitting Jan?
![Page 32: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/32.jpg)
Example 2
Jan steps into the road, 30 metres from where Mr Blanchard’s engine stops working. Mr Blanchard does not see Jan. Will the car stop in time to miss hitting Jan?
What does the question tell us. Write it out.
![Page 33: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/33.jpg)
Example 2
Jan steps into the road, 30 metres from where Mr Blanchard’s engine stops working. Mr Blanchard does not see Jan. Will the car stop in time to miss hitting Jan?
u = 10 ms-1
v = 0 ms-1
a = -2 ms-2
t = 5 ss = ? m
![Page 34: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/34.jpg)
Example 2
Jan steps into the road, 30 metres from where Mr Blanchard’s engine stops working. Mr Blanchard does not see Jan. Will the car stop in time to miss hitting Jan?
u = 10 ms-1 v = 0 ms-1 a = -2 ms-2 t = 5 s s = ? m
Choose the equation that has these quantities in
v2 = u2 + 2as
![Page 35: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/35.jpg)
Example 2
Jan steps into the road, 30 metres from where Mr Blanchard’s engine stops working. Mr Blanchard does not see Jan. Will the car stop in time to miss hitting Jan?
u = 10 ms-1 v = 0 ms-1 a = -2 ms-2 t = 5 s s = ? m
v2 = u2 + 2as
02 = 102 + 2x-2s
0 = 100 -4s
4s = 100
s = 25m, the car does not hit Jan.
![Page 36: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/36.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
![Page 37: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/37.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
• When is the velocity of the ball 12 m.s-1?
![Page 38: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/38.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
• When is the velocity of the ball 12 m.s-1?
u = 24 m.s-1 a = -9.8 m.s-2 v = 12 m.s-1
t = ?
![Page 39: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/39.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
• When is the velocity of the ball 12 m.s-1?
u = 24 m.s-1 a = -9.8 m.s-2 v = 12 m.s-1
t = ?
v = u + at
![Page 40: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/40.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-
1. • When is the velocity of the ball 12 m.s-1?
u = 24 m.s-1 a = -9.8 m.s-2 v = 12 m.s-1
v = u + at
12 = 24 + -9.8t
-12 = -9.8t
t = 12/9.8 = 1.2 seconds
![Page 41: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/41.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
• When is the velocity of the ball -12 m.s-1?
![Page 42: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/42.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
• When is the velocity of the ball -12 m.s-1?
u = 24 m.s-1 a = -9.8 m.s-2 v = -12 m.s-1
t = ?
![Page 43: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/43.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
• When is the velocity of the ball -12 m.s-1?
u = 24 m.s-1 a = -9.8 m.s-2 v = -12 m.s-1
v = u + at
![Page 44: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/44.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-
1. • When is the velocity of the ball -12 m.s-1?
u = 24 m.s-1 a = -9.8 m.s-2 v = -12 m.s-1
v = u + at
-12 = 24 + -9.8t
-36 = -9.8t
t = 36/9.8 = 3.7 seconds
![Page 45: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/45.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
• What is the displacement of the ball at those times? (t = 1.2, 3.7)
![Page 46: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/46.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
• What is the displacement of the ball at those times? (t = 1.2, 3.7)
t = 1.2, v = 12, a = -9.8, u = 24 s = ?
![Page 47: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/47.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
• What is the displacement of the ball at those times? (t = 1.2, 3.7)
t = 1.2, v = 12, a = -9.8, u = 24 s = ?
s = ut + ½at2 = 24x1.2 + ½x-9.8x1.22
s = 28.8 – 7.056 = 21.7 m
![Page 48: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/48.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
• What is the displacement of the ball at those times? (t = 1.2, 3.7)
t = 3.7, v = 12, a = -9.8, u = 24 s = ?
s = ut + ½at2 = 24x3.7 + ½x-9.8x3.72
s = 88.8 – 67.081 = 21.7 m (the same?!)
![Page 49: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/49.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
• What is the velocity of the ball 1.50 s after launch?
![Page 50: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/50.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
• What is the velocity of the ball 1.50 s after launch?
u = 24, t = 1.50, a = -9.8, v = ?
![Page 51: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/51.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
• What is the velocity of the ball 1.50 s after launch?
u = 24, t = 1.50, a = -9.8, v = ?
v = u + at
![Page 52: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/52.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
• What is the velocity of the ball 1.50 s after launch?
u = 24, t = 1.50, a = -9.8, v = ?
v = u + at
v = 24 + -9.8x1.50 = 9.3 m.s-1
![Page 53: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/53.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
• What is the maximum height reached by the ball?
![Page 54: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/54.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
• What is the maximum height reached by the ball?
u = 24, a = -9.8, v = 0, s = ?
![Page 55: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/55.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
• What is the maximum height reached by the ball?
u = 24, a = -9.8, v = 0, s = ?
v2 = u2 + 2as
0 = 242 + 2x-9.8xs
0 = 242 -19.6s
![Page 56: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/56.jpg)
Example 3
• A ball is thrown upwards with a velocity of 24 m.s-1.
• What is the maximum height reached by the ball?
u = 24, a = -9.8, v = 0, s = ?
0 = 242 -19.6s
19.6s = 242
s = 242/19.6 = 12.3 m
![Page 57: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/57.jpg)
Imagine a dog being thrown out of an aeroplane.
Woof! (help!)
![Page 58: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/58.jpg)
Force of gravity means the dog accelerates
gravityTo start, the dog is falling slowly (it has not had time to speed up).
There is really only one force acting on the dog, the force of gravity.
The dog falls faster (accelerates) due to this force.
![Page 59: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/59.jpg)
Gravity is still bigger than air resistance
gravity
As the dog falls faster, another force becomes bigger – air resistance.
The force of gravity on the dog of course stays the same
The force of gravity is still bigger than the air resistance, so the dog continues to accelerate (get faster)
Air resistance
![Page 60: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/60.jpg)
Gravity = air resistanceTerminal velocity
gravity
As the dog falls faster and air resistance increases, eventually the air resistance becomes as big as (equal to) the force of gravity.
The dog stops getting faster (accelerating) and falls at constant velocity.
This velocity is called the terminal velocity.
Air resistance
![Page 61: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/61.jpg)
Falling without air resistance
gravity
This time there is only one force acting in the ball - gravity
![Page 62: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/62.jpg)
Falling without air resistance
gravity
The ball falls faster….
![Page 63: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/63.jpg)
Falling without air resistance
gravity
The ball falls faster and faster…….
![Page 64: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/64.jpg)
Falling without air resistance
gravity
The ball falls faster and faster and faster…….
It gets faster by 9.81 m/s every second (9.81 m/s2)
This number is called “g”, the acceleration due to gravity.
![Page 65: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/65.jpg)
Falling without air resistance?
distance
time
![Page 66: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/66.jpg)
Falling without air resistance?
speed
time
Gradient = acceleration = 9.8 m.s-2
![Page 67: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/67.jpg)
Velocity/time graphs
Taking upwards are the positive direction
velocity/m.s-1
Time/s
Ball being thrown into the air, gradient = constant = -9.81 m.s-2
![Page 68: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/68.jpg)
Falling with air resistance?
distance
time
![Page 69: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/69.jpg)
Falling with air resistance?
velocity
time
Terminal velocity
![Page 70: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/70.jpg)
Gravity
What is gravity?
![Page 71: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/71.jpg)
Gravity
Gravity is a force between ALL objects!
Gravity
![Page 72: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/72.jpg)
Gravity
The size of the force depends on the mass of the objects. The bigger they are, the bigger the force!
Small attractive force
Bigger attractive force
![Page 73: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/73.jpg)
Gravity
The size of the force also depends on the distance between the objects.
![Page 74: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/74.jpg)
Gravity
We only really notice the gravitational attraction to big objects!
Hola! ¿Como estas?
![Page 75: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/75.jpg)
Gravity
The force of gravity on something is called its weight. Because it is a force it is measured in Newtons.
Weight
![Page 76: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/76.jpg)
Gravity
On the earth, Mr George’s weight is around 800 N.
800 N
I love physics!
![Page 77: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/77.jpg)
Gravity
On the moon, his weight is around 130 N.
Why?
130 N
![Page 78: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/78.jpg)
Gravity
In deep space, far away from any planets or stars his weight is almost zero. (He is weightless). Why?
Cool!
![Page 79: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/79.jpg)
Mass
Mass is a measure of the amount of material an object is made of and also its resistance to motion (inertia). It is measured in kilograms.
![Page 80: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/80.jpg)
Mass
Mr George has a mass of around 77 kg. This means he is made of 77 kg of blood, bones, hair and poo!
77kg
![Page 81: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/81.jpg)
Mass
On the moon, Mr George hasn’t changed (he’s still Mr George!). That means he still is made of 77 kg of blood, bones, hair and poo!
77kg
![Page 82: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/82.jpg)
Gravity
In deep space, Mr George still hasn’t changed (he’s still Mr George!). That means he still is made of 77 kg of blood, bones, hair and poo!
77kgI feel sick!
![Page 83: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/83.jpg)
Calculating weight
To calculate the weight of an object you multiply the object’s mass by the gravitational field strength wherever you are.
Weight (N) = mass (kg) x gravitational field strength (N/kg)
![Page 84: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/84.jpg)
Newton’s 1st Law
An object continues in uniform motion in a straight line or at rest unless a resultant external force acts
![Page 85: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/85.jpg)
Newton’s first law
Galileo imagined a marble rolling in a very smooth (i.e. no friction) bowl.
![Page 86: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/86.jpg)
Newton’s first lawIf you let go of the ball, it always rolls up the opposite side until it reaches its original height (this actually comes from the conservation of energy).
![Page 87: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/87.jpg)
Newton’s first lawNo matter how long the bowl, this always happens.
constant velocity
![Page 88: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/88.jpg)
Newton’s first lawGalileo imagined an infinitely long bowl where the ball never reaches the other side!
![Page 89: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/89.jpg)
Newton’s first lawThe ball travels with constant velocity until its reaches the other side (which it never does!).
Galileo realised that this was the natural state of objects when no (resultant ) forces act.
constant velocity
![Page 90: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/90.jpg)
Another example
Imagine Mr George cycling at constant velocity.
![Page 91: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/91.jpg)
Newton’s 1st law
He is providing a pushing force.
Constant velocity
![Page 92: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/92.jpg)
Newton’s 1st law
There is an equal and opposite friction force.
Constant velocity
Pushing force
friction
![Page 93: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/93.jpg)
Newton’s second law
Newton’s second law concerns examples where there is a resultant force.
![Page 94: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/94.jpg)
Let’s go back to Mr George on his bike.
Remember when the forces are balanced (no resultant force) he travels at constant velocity.
Constant velocity
Pushing force
friction
![Page 95: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/95.jpg)
Newton’s 2nd law
Now lets imagine what happens if he pedals faster.
Pushing force
friction
![Page 96: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/96.jpg)
Newton’s 2nd law
His velocity changes (goes faster). He accelerates!
Pushing force
friction
acceleration
Remember from last year that acceleration is rate of change of velocity. In other words
acceleration = (change in velocity)/time
![Page 97: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/97.jpg)
Newton’s 2nd law
Now imagine what happens if he stops pedalling.
friction
![Page 98: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/98.jpg)
Newton’s 2nd law
So when there is a resultant force, an object accelerates (changes velocity)
Pushing force
friction
Mr George’s Porche
![Page 99: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/99.jpg)
Newton’s 2nd lawThere is a mathematical relationship between the resultant force and acceleration.
Resultant force (N) = mass (kg) x acceleration (ms-2)
FR = maIt’s physics, there’s
always a mathematical relationship!
![Page 100: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/100.jpg)
An example
Resultant force = 100 – 60 = 40 N
FR = ma
40 = 100a
a = 0.4 m/s2
Pushing force (100 N) Friction (60
N)
Mass of Mr George and bike = 100 kg
![Page 101: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/101.jpg)
Newton’s 3rd lawIf a body A exerts a force on body B, body B will exert an equal but opposite force on body A.
Hand (body A) exerts force on table (body B)
Table (body B) exerts force on hand (body A)
![Page 102: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/102.jpg)
Free-body diagrams
Shows the magnitude and direction of all forces acting on a single body
The diagram shows the body only and the forces acting on it.
![Page 103: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/103.jpg)
Examples
• Mass hanging on a rope
W (weight)
T (tension in rope)
![Page 104: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/104.jpg)
Examples
• Inclined slope
W (weight)
R (normal reaction force)F
(friction)
If a body touches another body there is a force of reaction or contact force. The force is perpendicular to the body exerting the force
![Page 105: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/105.jpg)
Examples
• String over a pulley
T (tension in rope)
T (tension in rope)
W
1
W
1
![Page 106: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/106.jpg)
Momentum
• Momentum is a useful quantity to consider when thinking about "unstoppability". It is also useful when considering collisions and explosions. It is defined as
Momentum (kg.m.s-1) = Mass (kg) x Velocity (m.s-1)
p = mv
![Page 107: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/107.jpg)
Law of conservation of momentum
• The law of conservation of linear momentum says that
“in an isolated system, momentum remains constant”.
We can use this to calculate what happens after a collision (and in fact during an “explosion”).
![Page 108: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/108.jpg)
Law of conservation of momentum
• In a collision between two objects, momentum is conserved (total momentum stays the same). i.e.
Total momentum before the collision = Total momentum after
Momentum is not energy!
![Page 109: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/109.jpg)
A harder example!
• A car of mass 1000 kg travelling at 5 m.s-1 hits a stationary truck of mass 2000 kg. After the collision they stick together. What is their joint velocity after the collision?
![Page 110: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/110.jpg)
A harder example!
5 m.s-1
1000kg
2000kgBefore
AfterV m.s-1
Combined mass = 3000 kg
Momentum before = 1000x5 + 2000x0 = 5000 kg.m.s-1
Momentum after = 3000v
![Page 111: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/111.jpg)
A harder example
The law of conservation of momentum tells us that momentum before equals momentum after, so
Momentum before = momentum after
5000 = 3000v
V = 5000/3000 = 1.67 m.s-1
![Page 112: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/112.jpg)
Momentum is a vector
• Momentum is a vector, so if velocities are in opposite directions we must take this into account in our calculations
![Page 113: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/113.jpg)
An even harder example!
Snoopy (mass 10kg) running at 4.5 m.s-
1 jumps onto a skateboard of mass 4 kg travelling in the opposite direction at 7 m.s-1. What is the velocity of Snoopy and skateboard after Snoopy has jumped on?
I love physics
![Page 114: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/114.jpg)
An even harder example!
10kg
4kg-4.5 m.s-1
7 m.s-1
Because they are in opposite directions, we make one velocity negative
14kg
v m.s-1
Momentum before = 10 x -4.5 + 4 x 7 = -45 + 28 = -17
Momentum after = 14v
![Page 115: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/115.jpg)
An even harder example!
Momentum before = Momentum after
-17 = 14v
V = -17/14 = -1.21 m.s-1
The negative sign tells us that the velocity is from left to right (we choose this as our “negative direction”)
![Page 116: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/116.jpg)
“Explosions” - recoil
![Page 117: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/117.jpg)
ImpulseFt = mv – mu
The quantity Ft is called the impulse, and of course mv – mu is the change in momentum (v = final
velocity and u = initial velocity)
Impulse = Change in momentum
![Page 118: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/118.jpg)
ImpulseFt = mv – mu
F = Δp/Δt
![Page 119: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/119.jpg)
Units
Impulse is measured in N.s (Ft)
or kg.m.s-1 (mv – mu)
![Page 120: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/120.jpg)
ImpulseNote; For a ball bouncing off a wall, don’t forget
the initial and final velocity are in different directions, so you will have to make one of them
negative.
In this case mv – mu = -3m -5m = -8m
5 m/s
-3 m/s
![Page 121: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/121.jpg)
Example
• Szymon punches Eerik in the face. If Eerik’s head (mass 10 kg) was initially at rest and moves away from Szymon’s fist at 3 m/s, what impulse was delivered to Eerik’s head? If the fist was in contact with the face for 0.2 seconds, what was the force of the punch?
• m = 10kg, t = 0.2, u = 0, v = 3
• Impulse = Ft = mv – mu = 10x3 – 10x0 = 30 Ns
• Impulse = Ft = 30
Fx0.2 = 30
F = 30/0.2 = 150 N
![Page 122: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/122.jpg)
Another example
• A tennis ball (0.3 kg) hits a racquet at 3 m/s and rebounds in the opposite direction at 6 m/s. What impulse is given to the ball?
• Impulse = mv – mu == 0.3x-6 – 0.3x3
= -2.7kg.m.s-1
3 m/s
-6 m/s
![Page 123: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/123.jpg)
Area under a force-time graph = impulse
Area = impulse
![Page 124: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/124.jpg)
Work
In physics, work has a special meaning, different to “normal” English.
![Page 125: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/125.jpg)
Work
In physics, work is the amount of energy transformed (changed) when a force moves (in the direction of the force)
![Page 126: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/126.jpg)
Calculating work
The amount of work done (measured in Joules) is equal to the force used (Newtons) multiplied by the distance the force has moved (metres). Force (N)
Distance travelled (m)
![Page 127: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/127.jpg)
Work (J)= Force(N) x distance(m)
W = Fscosθ
![Page 128: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/128.jpg)
Important
The force has to be in the direction of movement. Carrying the shopping home is not work in physics!
![Page 129: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/129.jpg)
Work = Fscosθ
s
F
θ
What if the force is at an angle to the distance moved?
![Page 130: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/130.jpg)
Lifting objects
Our lifting force is equal to the weight of the object.
Lifting force
weight
![Page 131: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/131.jpg)
Work done (J) = Force (N) x distance (m)
A woman pushes a car with a force of 400 N at an angle of 10° to the horizontal for a distance of 15m. How much work has she done?
W = Fscosθ = 400x15x0.985
W = 5900 J
![Page 132: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/132.jpg)
Work done (J) = Force (N) x distance (m)
A man lifts a mass of 120 kg to a height of 2.5m. How much work did he do?
Force = weight = 1200N
Work = F x d = 1200 x 2.5
Work = 3000 J
![Page 133: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/133.jpg)
Power!
Power is the amount of energy transformed (changed) per second. It is measured in Watts (1 Watt = 1 J/s)
Power = Energy transformed
time
![Page 134: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/134.jpg)
Work done in stretching a spring
F/N
x/m
Work done in strectching spring = area under graph
![Page 135: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/135.jpg)
Chemical kinetic gravitational
Gain in GPE = work done = m x g x Δh
![Page 136: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/136.jpg)
ΔEp = mgΔh
Joules kgN/kg or m/s2
m
![Page 137: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/137.jpg)
Example
A dog of mass 12 kg falls from an aeroplane at a height of 3.4 km. How much gravitational energy does the dog lose as it falls to the ground
Woof! (help!)
![Page 138: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/138.jpg)
ExampleOn earth g = 10 m/s2
Height = 3.4 km = 3400 m
Mass of dog = 12 kg
![Page 139: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/139.jpg)
ExampleOn earth g = 10 m/s2
Height = 3.4 km = 3400 m
Mass of dog = 12 kg
GPE lost by dog = mgh = 12 x 10 x 3400 = 408 000 J
![Page 140: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/140.jpg)
Example
GPE lost by dog = mgh = 12 x 10 x 3400 = 408 000 J
Just before the dog hits the ground, what has this
GPE turned into?
![Page 141: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/141.jpg)
Kinetic energy
Kinetic energy of an object can be found using the following formula
Ek = mv2
2where m = mass (in kg) and v = speed (in m/s)
![Page 142: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/142.jpg)
Example
A bullet of mass 150 g is travelling at 400 m/s. How much kinetic energy does it have?
Ek = mv2/2 = (0.15 x (400)2)/2 = 12 000 J
![Page 143: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/143.jpg)
Energy changes
![Page 144: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/144.jpg)
Energy transfer (change)
A lamp turns electrical energy into heat and light energy
![Page 145: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/145.jpg)
Sankey Diagram
A Sankey diagram helps to show how much light and heat energy is produced
![Page 146: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/146.jpg)
Sankey Diagram
The thickness of each arrow is drawn to scale to show the amount of energy
![Page 147: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/147.jpg)
Sankey Diagram
Notice that the total amount of energy before is equal to the total amount of energy after (conservation of energy)
![Page 148: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/148.jpg)
Efficiency
Although the total energy out is the same, not all of it is useful.
![Page 149: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/149.jpg)
Efficiency
Efficiency is defined as
Efficiency = useful energy output
total energy input
![Page 150: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/150.jpg)
Example
Efficiency = 75 = 0.15=15%
500
![Page 151: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/151.jpg)
Energy efficient light bulb
Efficiency = 75 = 0.75
100 That’s much better!
![Page 152: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/152.jpg)
Elastic collisions
• No loss of kinetic energy (only collisions between subatomic particles)
![Page 153: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/153.jpg)
Inelastic collisions
• Kinetic energy lost (but momentum stays the same!)
![Page 154: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/154.jpg)
Satellites
![Page 155: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/155.jpg)
How far could you kick a dog?
From a table, medium kick.
![Page 156: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/156.jpg)
How far can you kick a dog?
Gravity
![Page 157: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/157.jpg)
Harder kick
Gravity
![Page 158: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/158.jpg)
Small cannon
Gravity
Woof! (help)
![Page 159: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/159.jpg)
Bigger cannon
GravityGravity
![Page 160: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/160.jpg)
Even bigger cannon
GravityGravity
Gravity
![Page 161: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/161.jpg)
VERY big cannon
Gravity
![Page 162: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/162.jpg)
Humungous cannon?
![Page 163: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/163.jpg)
Dog in orbit!
The dog is now in orbit! (assuming no air resistance of course)
![Page 164: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/164.jpg)
Dog in orbit!
The dog is falling towards the earth, but never gets there!
![Page 165: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/165.jpg)
Dogs in orbit!
The force that keeps an object moving in a circle is called the centripetal force (here provided by gravity)
Gravity
![Page 166: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/166.jpg)
Other examples
Earth’s gravitational attraction on moon
![Page 167: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/167.jpg)
Uniform Circular Motion
• This describes an object going around a circle at constant speed
![Page 168: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/168.jpg)
Direction of centripetal acceleration/force
VA
VB
VAVB
VA + change in velocity = VB
Change in velocity
The change in velocity (and thus the acceleration) is directed towards the centre of the circle.
![Page 169: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/169.jpg)
Uniform circular motion
The centripetal acceleration/force is always directed towards the centre of the circle
Centripetal force/acceleration
velocity
![Page 170: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/170.jpg)
Not uniform velocity
• It is important to remember that though the speed is constant, the direction is changing all the time, so the velocity is changing.
Uniform speed ≠ uniform velocity
![Page 171: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/171.jpg)
How big is the centripetal acceleration?
a = v2 = 4π2r
r T2
where a is the centripetal acceleration (m.s-2), r is the radius of the circle (m), and v is the constant speed (m.s-1).
![Page 172: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/172.jpg)
How big is the centripetal force?
F = mv2
r
from F = ma (Newton’s 2nd law)
Centripetal Force - The Real Force
![Page 173: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/173.jpg)
Work done?
• None! Because the force is always perpendicular to the motion, no work is done by the centripetal force.
![Page 174: Distance against time graphs distance time. Constant speed distance time The gradient of this graph gives the speed.](https://reader037.fdocuments.in/reader037/viewer/2022102619/56649e8a5503460f94b8f705/html5/thumbnails/174.jpg)
That’s it!