Post on 29-Dec-2015
a = Velocityfinal – Velocityinitial
time
Solve for Velocityfinal with algebra
A new (but old) formula
Velocityfinal= Velocityinitial + at
Velocityfinal= Velocityinitial + at
Calculate the instantaneous speed at the 10 s mark for a car that accelerates at 2 m/s² from a position at rest
Velocityfinal= Velocityinitial + at = 0 m/s +2 m/s² (10 s) = 20 m/s
Free Fall
Definition- when an object is moving solely (only) under the influence of gravity….
Example of gravity
Dropping a ball?
Throwing a ball?
Yes
Yes, once it leaves your hand
Experience tells you that objects speed up (or accelerate) as they fall
All objects always accelerate at the same rate
(when we ignore air resistance)
Ignoring air resistance
On the moon
http://www.youtube.com/watch?v=U7db6ZeLR5s
So what is that magical number that all objects accelerate at?
9.8 m/s²
Finish the definition of free fall
Definition- when an object is moving solely (only) under the influence of gravity….
(when we ignore air resistance)
The History of the Law of Falling Bodies
Galileo Galilei
(1564-1642)
Galileo is said to have dropped two unequal weights from the top of the Leaning Tower of Pisa to prove his theory. Galileo claimed that a naturally falling object would gain equal amounts of velocity in equal amounts of time.
If correct, this means that i) the object’s speed increases as it falls and ii) the rate at which it picks up speed does not change during the fall.
However, for medieval science, freely falling objects moved too quickly and the clocks could not record quickly enough .
So Galileo devised to slow down the motion by replacing thefalling object with a ball rolling down a gently inclined plane.
The velocity of a free-falling object which has been dropped from a position of rest is
dependent upon the time for which it has fallen.
Time (s) Velocity (m/s) 0 0 1 9.8 2 19.6
3 29.4
4 39.2
5 49.0
Gravity
1) Causes free falling objects to accelerate at 9.8 m/s² toward the center of the earth.
2) The symbol is g (for acceleration due to gravity)
GravityPositive or
negative?...that’s the question!
By convention….+ 9.8 when an object
is falling towards the earth
- 9.8 when an object is moving away from the earth
How fast something is moving is very different from how far
How far does an object fall in 1 s?
It is 4.9 m….why?
In free fall, the object started from rest and is not at a constant speed
Velocityavg=Vfinal + Vinitial
2
How far will an object drop?
d= ½ gt²
I drop a rock off of a bridge, and 4.2 s later, I hear a splash. What is the height of the bridge?
d= ½ (9.8 m/s²) (4.2 s)²
= 86 m
Kinematics Formula Summary
1. vf = vi + g t
2. d = vi t + ½½g t
2 if velocity is 0 then the equation
3. vf2 = vi
2 + 2 gd
Practice Problem
You drop a ball from rest off a 120 m high cliff. Assuming air resistance is negligible (free fall), how long is the ball in the air?
What is the ball’s speed when it strikes the ground at the base of the cliff?
Answer
t = 4.95s
vf =48.5m/s
Reviewhttp://onlinephys.com
/freefall6.gif
http://onlinephys.com/freefall5.gif
What’s the story?
Free Fall with Upward Motion
• When something is thrown straight upward under the influence of gravity, and then returns to the thrower, this is very symmetrical = parabola
• The object spends half its time traveling up; half traveling down.
Free Fall with Upward Motion
• Velocity when it returns to the ground is the opposite of the velocity it was thrown upward with.
• Acceleration is 9.8 m/s2 and directed DOWN the entire time the object is in the air!
Free Fall with Upward Motion
Free Fall with Upward Motion
Homer Hickham used this fact to determine how high his rocket went and that the rocket boys didn’t start the fire in Welch
October Sky
http://www.youtube.com/watch?v=udHB3tftPz4