Post on 13-Jul-2018
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7-Sep-10 Physics 101
Chapters 5 & 6More Third Law
Vectors at AnglesMomentum
Conservation of Momentum
Lecture 6
7-Sep-10 Physics 101
Announcements
• Help sessions– M 1600-1700 in TH116 (A. Kelly)– M 1700-1900 in TH116 (D. Lim)– T 1600-1700 in TH118 (Z. Hadley)– W 1510-1600 in TH118 (J.M. Lockhart)
• Course web pagewww.physics.sfsu.edu/~lockhart/courses/phys101.html
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7-Sep-10 Physics 101
IMPORTANT!!!
Action force & reaction force NEVER cancel, because they act on different objects!
Repeat this to yourself over and over again
7-Sep-10 Physics 101
Check YourselfMiss A pushes the car (action);
car pushes back on her (reaction). Do these forces cancel?
Force on Miss A is to the left; how can she move forward (to the right)?
What if floor had zero friction?
Miss A
Action
Reaction
Action
Reaction
Action-Reaction
Pairs
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7-Sep-10 Physics 101
Check YourselfMiss B also pushes the car;
can she move the car by herself?
In terms of Newton’s laws, why is this not possible?
What other force does Miss B exert on the car besides her hands?
Miss BAction
ReactionReaction
Action
Action-Reaction
Pairs
7-Sep-10 Physics 101
Adding Forces
When two forces or more forces act in different directions, finding the net force is more complicated.
Have to consider the angle for each force.
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7-Sep-10 Physics 101
Parallelogram rule
Vector Addition
Forces are vectors, with magnitude & direction. How two vectors add together depends on the two magnitudes and the two directions.
Object Force A(20 Newtons)
Force B(10 N)
Net ForceA + B
(25 Newtons)
7-Sep-10 Physics 101
Magnitude & Angle of Vector SumMagnitude & Angle of Vector SumVector magnitude and angle of the sum of two perpendicular vectors can be calculated using trigonometry and Pythagorean theorem:
2 2x yA A A= +1tan /y xA Aθ −=
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7-Sep-10 Physics 101
Magnitude & Angle ExampleMagnitude & Angle Example
Polar CoordinatesCartesian Coordinates
2 2 2 2 2(1.36 m) (0.634 m) 2.25 m 1.50 mx yr r r= + = + = =
[ ]1 1tan (0.634 m) / (1.36 m) tan (0.466) 25.0θ − −= = = °
7-Sep-10 Physics 101
Demo: Straighten the Line
Pull on the line to make it horizontal.
15 poundBowling Ball
PullPull
HORIZONTAL
As the angle gets smaller, must pull muchharder.
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7-Sep-10 Physics 101
Demo: Straighten the Line (II)
10 NewtonWeight
5 N5 N
10 NewtonWeight
15 N15 N
As the angle gets smaller, must pull muchharder.
7-Sep-10 Physics 101
Parallelogram Rule
Weight
pullpullPULL! PULL!
Net Force
Net force is the same in both cases but pulling forces different.
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7-Sep-10 Physics 101
Nellie Newton hangs motionless by one hand from a clothesline — which is on the verge of breaking. Which side of the line is more likely to break?
1. Left side2. Right side3. 50/50 chance
of either side breaking
Check Yourself
Two upward forces must add together to balance Nellie’s weight.
7-Sep-10 Physics 101
Lab: Force Table
Practice addition of forces as vectors in the Physics 102 lab using “force tables.”
Hang weights and adjust angles until forces balance.
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7-Sep-10 Physics 101
Force, Momentum, Energy
With Newton’s Laws, we can understand motion just using forces. Can also eat food just using knives or chopsticks.
Easier to understand motion by introducing concepts of momentum and energy. Think of them as the fork and spoon of mechanics.
7-Sep-10 Physics 101
Momentum“Inertia of Motion”
Momentum of an object is:(Momentum) =
(Mass) X (Velocity)Vector quantity; direction isdirection of velocitySI Unit: kg•m/sExamples of objects with large
momenta: supertanker (large mass); bullet (large velocity).
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7-Sep-10 Physics 101
Momentum Example
• A 0.25 kg baseball is moving North at 10 m/s. What is its momentum?
• Momentum = mv = (0.25 kg)(10 m/s North)= 2.5 kg•m/s North
7-Sep-10 Physics 101
Check YourselfA 2 ton car, going 60 m.p.h. hits 5 ton truck, going 20 m.p.h..Which vehicle, car or truck, has greater momentum?
What would the car’s speed have to be for the momenta to match?
Aren’t you forgetting something?
How does that matter?
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7-Sep-10 Physics 101
Momentum and Force
To stop an object with a large momentum requires either:
• Large force (stopping the object quickly).• Small force applied for a long time.
Notice that changing object’s momentum depends on force and time interval.
7-Sep-10 Physics 101
Impulse
Define impulse acting on an object as
(Impulse) = (Force on object) X (Time interval for force )
Objects have momentum.Impulse acts on an object.
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7-Sep-10 Physics 101
Impulse & Momentum
Impulse is related to momentum by,
(Change in momentum) = (Impulse)or
(Mass) X (Change in velocity) =(Force) X (Time interval)
This relation comes from Newton’s 2nd law.
7-Sep-10 Physics 101
Check YourselfThrow egg at sheet or wall with
same speed. Which case has:Greater change of velocity?
Greater change of momentum?
Largest impulse on the egg?
Largest time of impact?
Largest force on the egg?
LONG TIME
short time
small force
LARGE FORCE
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7-Sep-10 Physics 101
Demo: Vampire StakeSafest when slow moving stake is placed on a soft,
fleshy spot on the chest.
(force) x (TIME)
X XOuch!
(FORCE) x (time)
Not safe if stake strikes hard skull
7-Sep-10 Physics 101
Check YourselfA 2 ton car going 60 m.p.h. hits 5 ton truck going 20 m.p.h..
Force of impact is greatest on which vehicle, car or truck?
Impulse is greatest on which vehicle, car or truck?
Change of momentum greatest?
Change of velocity greatest?
Driver injury greatest?
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7-Sep-10 Physics 101
Automobile SafetyMaximizing the time of impact on the driver minimizes
the force of impact. This principle used in design of:
Seatbelts Air Bags CrumpleZones
7-Sep-10 Physics 101
Conservation of Momentum
The principle of conservation of momentum states: When there is no net external force on a system of objects, the total momentum of the system does not change.
We say that the momentum of such a system is conserved since it does not change.
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7-Sep-10 Physics 101
Conservation of Momentum in Collisions
When two objects collide, impulse is equal and opposite for the two objects if there is no net external force.
Before collision
Impact
After collision
IMPULSEIMPULSE
Each object has equal and opposite change in momentum.The momentum of the system of 2 objects is conserved.
7-Sep-10 Physics 101
Conservation of MomentumThe change of momentum of the two objects in a collision
is equal and opposite -- the momentum gained by one object is the amount lost by the other.
MomentumObject A
Before Collision
MomentumObject B
Before Collision+
A B
MomentumObject A
After Collision
MomentumObject B
After Collision= +
A B
Actual amount of momentum exchanged depends on the details of the collision, such as whether or not collision is elastic, but total momentum is always conserved if there is no net external force.
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7-Sep-10 Physics 101
Demo: Elastic CollisionsObjects of equal mass exchange momentum in
elastic collisions.
7-Sep-10 Physics 101
Demo: Newton’s Balls
Steel balls collide elastically, exchanging momentum on collision.
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7-Sep-10 Physics 101
Demo: Don’t ScratchTo sink a billiard ball that is very close to the
pocket without having the cue ball go in as well (“scratching”), strike the cue ball hard so it makes a crisp, elastic collision.
As with Newton’s balls, cue ball will stop after giving all its momentum to the other ball in the collision.
7-Sep-10 Physics 101
Demo: Blaster Balls
When masses unequal, momentum change can be large.
Pingpongball
Golfball
Speed ofping-pong ball
is 3x larger(Slingshot effect)
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7-Sep-10 Physics 101
Demo: Inelastic CollisionsObjects stick together after colliding.
A
A
A
B
B
B
7-Sep-10 Physics 101
Check Yourself
Large (4 kg) fish swims at 3 m/s towards a small (2 kg) fish (at rest) and swallows it for lunch.
Total momentum before lunch?
Total momentum after lunch?
Velocity of the large fish (with small fish inside)?
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7-Sep-10 Physics 101
Recoil
Momentum conservation also explains recoil
(MASS) x (velocity) (mass) x (VELOCITY)
Recoil effect is like an inelastic collision in reverse.
7-Sep-10 Physics 101
Key Points of Lecture 6Key Points of Lecture 6
Before next lecture, read Hewitt through Chap.6
Homework Assignment #3 is due before 11:00 PM on Thursday, Sept. 9.
• Third Law Details• Combining Two Perpendicular Vectors• Momentum (Mass•Velocity)• Impulse (Force•time_applied)
•Impulse = momentum change• Conservation of momentum• Collisions