lecture 6 chapters 5 & 6 - sfsu physics &...

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7-Sep-10 Physics 101

Chapters 5 & 6More Third Law

Vectors at AnglesMomentum

Conservation of Momentum

Lecture 6


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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IMPORTANT!!!

Action force & reaction force NEVER cancel, because they act on different objects!

Repeat this to yourself over and over again


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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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


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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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)


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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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 − −= = = °


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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Demo: Straighten the Line (II)

10 NewtonWeight

5 N5 N

10 NewtonWeight

15 N15 N

As the angle gets smaller, must pull muchharder.


Parallelogram Rule

Weight

pullpullPULL! PULL!

Net Force

Net force is the same in both cases but pulling forces different.

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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.


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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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.


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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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


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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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.


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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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.


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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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


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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Automobile SafetyMaximizing the time of impact on the driver minimizes

the force of impact. This principle used in design of:

Seatbelts Air Bags CrumpleZones


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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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.


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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Demo: Elastic CollisionsObjects of equal mass exchange momentum in

elastic collisions.


Demo: Newton’s Balls

Steel balls collide elastically, exchanging momentum on collision.

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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.


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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Demo: Inelastic CollisionsObjects stick together after colliding.

A

A

A

B

B

B


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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Recoil

Momentum conservation also explains recoil

(MASS) x (velocity) (mass) x (VELOCITY)

Recoil effect is like an inelastic collision in reverse.


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

lecture 6 chapters 5 & 6 - sfsu physics &...

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