Momentum Is momentum in basketball physics? How do ...

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MomentumIs momentum in basketball physics?

Rockets and gunsHow do spaceships work?

Collisions of objectsThey get impulses!

Practical Propulsion

9/14/2016 Physics 214 Fall 2016 1

9/14/2016 Physics 214 Fall 2016 2

MomentumWhat happens when a force acts on an object

We know v = v0 + atSo that mv – mvo = mat

mv – mvo = Ft

The quantity mv is known as the momentum p and it is a vector quantity in the same direction as the velocity. The result of applying a force for a time t results in a change of momentum.

So a body moving with velocity v has kinetic energy = 1/2mv2 and momentum = mv

F

9/14/2016 Physics 214 Fall 2016 3

Conservation of Momentum

F1F2 F1 = -F2 and Δp1 + Δp2 = 0Total momentum is conserved

For a short interval of time t we have mv – mvo = Ft and

p = F tThis is the impulse equation

If we have a collision between two objects then in general the velocity of each object changes and kinetic energy is lost in the form of heat, sound or in a permanent deformation of the bodies.

9/14/2016 Physics 214 Fall 2016 4

1N-06 Equality of Momentum

THE SPRING FORCE THAT DRIVES THEM APART IS INTERNAL TO THE SYSTEM, SO THE NET MOMENTUM REMAINS ZERO.SINCE THE METAL CYLINDER IS HEAVIER IT FLIES AWAY WITH A SMALLER VELOCITY TO CONSERVE MOMENTUM

What happens when the spring

is released ?

First case: Both identical

Second case: One much heavier

Two cylinders are exploded apart by a spring

Use Momentum conservation m1v1 = m2v2The height reached is an indication of the initial speed since 1/2mv2 = mgh

v = sqrt (2gh)

9/14/2016 Physics 214 Fall 2016 5

1N-12 Fun Balls

NO MATTER HOW MANY BALLS ARE PULLED BACK, THE SAME NUMBER RECOIL AT THE SAME SPEED.

What happens when more of the balls are pulled

back than are left at rest?

An enlarged version of the Classic Toy - The Array of Steel Balls

The collision is nearly elastic so we can use both momentum conservation and kinetic energy conservation

What happens if we use the big ball?

First case pull back one ball and release

9/14/2016 Physics 214 Fall 2016 6

1N-04 Conservation of Linear Momentum

IF THE MASSES ARE IN INVERSE RATIO TO THE INITIAL DISTANCES, THE CARTS WILL ARRIVE AT THE STOPS SIMULTANEOUSLY.

T T

Is momentum conserved in this system ?

dA/dB = (vAtA) / (vBtB)

If, tA = tB dA/dB = mB / mA

vA / vB = mB / mA

Two carts move under tension of weight on frictionless track

The initial momentum of the carts is zero and they each feel equal and opposite forces. So at any time the net momentum will be zero.

0 = mAvA – mBvB mAvA = mBvB

9/14/2016 Physics 214 Fall 2016 7

Isolated systems

In each case m1v1 = - m2v2

anim0010.movhttp://www.physics.purdue.edu/academic_programs/courses/phys214/lectures/anim0010.mov

9/14/2016 Physics 214 Fall 2016 8

Momentum conservation

The conservation of momentum also is connected to the fundamental physical laws

The laws of physics do not change undertranslation or rotation in space

9/14/2016 Physics 214 Fall 2016 9

Impulse We have seen that a force F acting for a time ∆t changes momentum

F∆t = ∆p. F∆t is called an impulseThere are many situations where it is more useful to use the impulse when two objects collide than equating the change in momentum of each. In the case shown below the momentum of the earth changes but that is too difficult to calculate. It is better to use the fact that the earth exerts a force for a short time.

9/14/2016 Physics 214 Fall 2016 10

CollisionsIn a closed, isolated system containing a collision, the linear momentum of each colliding object can change but the total momentum of the system is a constant.

This statement is true even if energy is lost by the colliding bodies

*

9/14/2016 Physics 214 Fall 2016 11

Types of collisionElastic - no energy is lostInelastic - Energy is lost (transformed)Perfectly inelastic – objects stick togetherIn two dimensions momentum is conserved along

the x and y axes separately

y

x

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Perfectly Inelastic

Let initial velocity be vi and the mass of a car be m.Then

mvi = 3mvfinal and vfinal = vi/3

Kinetic Energy before = 1/2mvi2

Kinetic energy after = ½ x 3mv2final

So KEbefore/KEfinal = 3

9/14/2016 Physics 214 Fall 2016 13

Head on Elastic collisions

Pool ball collisions are close to being elasticv v

Pool ballsv

Bowling ball hits tennis ball

Tennis ball hits bowling ball

http://www.physics.purdue.edu/class/applets/phe/collision.htm

9/14/2016 Physics 214 Fall 2016 14

1N-10 Elastic & Inelastic Collisions

WE CAN MEASURE THE SPEED BY TIMING THE CARTS ACROSS A FIXED DISTANCE. For THE INELASTIC CASE HALF THE VELOCITY IMPLIES IT SHOULD TAKE TWICE THE TIME.

Elastic and Inelastic collisions of Two identical Carts on a Frictionless Track

How do the collisions compare?

Conservation of momentum mvA + mvB = mvA’ + mvB’

Conservation of Energy (Elastic)½ mvA

2 + ½ mvB2 = ½ mvA’2 + ½ mvB’2

If vB = 0 then vA’ = 0 and vB

’ = vA

Completely inelastic (two carts stick)if vB = 0 then vAB = ½ vA

9/14/2016 Physics 214 Fall 2016 15

1N-02 Collision of Two Large Balls

In practice some energy is always lost. You can hear the noise when they hit and there will be some heat generated at impact

Conservation of Energy (Elastic)½ mv1

2 + ½ mv22 = ½ mv1

2 + ½ mv22

v12 = v1A

2 + v2A2 v1A = 0 & v2A = v1Can we predict the

velocities of each ball after a collision ?

What happens when two large balls of equal mass collide one is at rest at the other has velocity v1?

Completely Inelastic collision (stick together)mv1 + mv2 = (m + m)vA (v2 =0)

v1 = 2vA vA = ½v1

Conservation of momentummv1 + mv2 = mv1A + mv2A v1 = v1A + v2A

9/14/2016 Physics 214 Fall 2016 16

1N-05 Elastic Collision (Magnets)

MOMENTUM TRANSFER AND CONSERVATION REQUIRE ONLY THAT THERE BE A MUTUAL INTERACTION. AT THE MICROSCOPIC LEVEL, ALL CONTACT INVOLVES ELECTROMAGNETIC INTERACTIONS.

We know that the magnets repel each other, so they will

not touch. So is this a collision?

SSv

Rest

SSv Rest

What does it mean for objects to ‘touch’ ?

Two Magnets collide with like poles facing each other

9/14/2016 Physics 214 Fall 2016 17

Collisions of Particles

Both energy and momentum and charge are conserved in elementary particle interactions and are a powerful tool in analyzing the fundamental physics. There are also other important conservation laws that for example prevent the proton from decaying.

9/14/2016 Physics 214 Fall 2016 18

Summary of Chapter 7The action of a force changes the momentum of an object

mv – mvo = Ft p = mv and is a vectorWhen two bodies interact they feel equal

and opposite forces

F1 = -F2 and Δp1 - Δp2 = 0Total momentum is conserved

9/14/2016 Physics 214 Fall 2016 19

Summary: ImpulseF∆t = ∆p is the impulse equation and is used to determine the momentum change when a force acts

Practical PropulsionA space vessel requires an engine and fuel or an external force. It has to be able to maneuver and be able to escape from the gravity of all objects that affect it’s path. Or, for example, to leave the moon after landing.

Conventional rockets are ~90% fuel by weight most of which is used escaping from the earth.

Very small satellites might be put into orbit using a powerful laser beam Nuclear engines are used in deep space probes. In this the radioactive

decay of the fuel emits particles which eject “backwards” and give the probe momentum. In this case it takes a long time to achieve high velocities

Solar sails have been tested which use enormous sails pushed by the solar wind of particles. This technique has limited application

Remember the nearest star is 4 light years away that is ~ 2 x 1013 miles or ~200,000 times the distance to the sun (ONE WAY!!)

Voyager just left the solar system after 36 years!!

9/14/2016 Physics 214 Fall 2016 20

9/14/2016 Physics 214 Fall 2016 21

Questions Chapter 7

Q5 Are impulse and momentum the same thing? Explain.

Q6 If a ball bounces off a wall so that its velocity coming back has the same magnitude that it had prior to bouncing:

A. Is there a change in the momentum of the ball? Explain.

B. Is there an impulse acting on the ball during its collision with the wall? Explain.

A. Yes momentum is a vector

B. Yes a force acts for a short time

No impulse changes momentum

9/14/2016 Physics 214 Fall 2016 22

Q9 What is the advantage of an air bag in reducing injuries during collisions? Explain using impulse and momentum ideas.

Q11 If you catch a baseball or softball with your bare hand, will the force exerted on your hand by the ball be reduced if you pull your arm back during the catch? Explain.

It increases the time over which the force acts.It also spreads the force over a larger area

Yes. The impulse is the same but the impact time is longer.From a work point of view the kinetic energy = Fd so increasing d reduces F

9/14/2016 Physics 214 Fall 2016 23

Q17 A compact car and a large truck have a head-on collision. During the collision, which vehicle, if either, experiences:

A. The greater force of impact? Explain.

B. The greater impulse? Explain.

C. The greater change in momentum? Explain.

D. The greater acceleration? Explain.

Q22 Is it possible for a rocket to function in empty space (in a vacuum) where there is nothing to push against except itself?

Yes. It ejects material at high velocity and momentum conservationmeans the rocket recoils

A. The forces are equal and oppositeB. The impulse for each is the sameC. The momentum changes are equal and oppositeD. F = ma so a is larger for the compact car

9/14/2016 Physics 214 Fall 2016 24

Q23 Suppose that you are standing on a surface that is so slick that you can get no traction at all in order to begin moving across this surface. Fortunately, you are carrying a bag of oranges. Explain how you can get yourself moving.

Q24 A railroad car collides and couples with a second railroad car that is standing still. If external forces acting on the system are ignored, is the velocity of the system after the collision equal to, greater than, or less than that of the first car before the collision?

Throw the oranges opposite to the direction you wish to move

The velocity after is exactly half

9/14/2016 Physics 214 Fall 2016 25

What is the momentum of a 1200 kg car traveling at 27 m/s?

P= mv = (1200 kg)(27 m/s)P = 32400 kg m/s M v

Ch 7 E 2

9/14/2016 Physics 214 Fall 2016 26

A ball experiences a change in momentum of 9.0 kg·m/s.a) What is the impulse?b) If the time of interaction = 0.15 s, what is the magnitude

of the average force on the ball?

a) Impulse = p = 9.0 kg m/s

b) Impulse = Ft, F = 9/0.15 = 60N

Ch 7 E 6

9/14/2016 Physics 214 Fall 2016 27

A ball has an initial momentum = 2.5 kg m/s, it bounces off a wall and comes back in opposite direction with momentum = -2.5 kg m/sa) What is the change in momentum of the ball?b) What is the impulse?

b) Impulse = ∆p = - 5kgm/s

a) ∆p = pf – pi = -2.5 – (+2.5) = - 5kgm/s

Ch 7 E 8

Pi = 2.5kgm/s

Pf = -2.5kgm/sF

+

9/14/2016 Physics 214 Fall 2016 28

M1 and M2 collide head ona) Find initial momentum of M1 and M2

b) What is the total momentum of the system before collision?

c) Ignore external forces, if they stick together after collision, which way do the masses travel?

a) p1 = -100 x 3.5 = - 350kgm/s p2 = 80 x 6 = 480kgm/s

b) Total momentum = 480 – 350 = 130kgm/s east

c) The masses will travel east with p = 130kgm/sec

6.0m/s 3.5m/sM1 = 100kgM2 = 80kg eastwest

Ch 7 E 10

9/14/2016 Physics 214 Fall 2016 29

M1 = 4000kg v1 = 10m/s due northM2 = 1200kg v2 = 20m/s due southMasses collide and stick.a) Find initial momentum of each mass.b) Find size and direction of momentum after

collision.

a) Call due north the +x directionp1 = m1 v1 = 4000 kg (10m/s) = 40000 kg m/sp2 = m2 v2 = 1200 kg (-20m/s) = - 24000 kg m/s

b) p = p1 + p2 = +16000 kg m/sThis is momentum of system before collision, but momentum is conserved. So after masses stick:p = 16000 kg m/s due North.

N

S

M2

M1

v2

v1

+x

Ch 7 E 16

9/14/2016 Physics 214 Fall 2016 30

y

x

1 2p p p 1p

2p

a) p1 = 40000kgm/s + y p2 = 30000kgm/s + x

A truck of mass 4000kg and speed 10m/s collides at rightangles with a car of mass 1500kg and a speed of 20m/s.a) Sketch momentum vectors before collisionb) Use vector addition to get total momentum of system

before collision.

b)

p1 = 40000

p2 = 30000

p

p2 = p12 + p2

2

P = 50000kgm/s

Ch 7 E 18

9/14/2016 Physics 214 Fall 2016 31

A bullet is fired into block sitting on ice. The bullet travels at500 m/s with mass 0.005 kg. The wooden block is at rest with amass of 1.2 kg. Afterwards the bullet is embedded in the block.a) Find the velocity of the block and bullet after the impact (assume

momentum is conserved).b) Find the magnitude of the impulse on the block of wood.c) Does the change in momentum of the bullet equal that of wood?

v

m MNo friction (ice)

b) Impulse = ∆p = pfinal – pinitial

= (1.2 kg)(2.07 m/s) – 0 = 2.50 kg m/sc) ∆p for bullet = (0.005 kg)(500 m/s) – (0.005 kg)(2.07 m/s)

= 2.50 kg m/sMomentum is conserved, so momentum lost by bullet is gained by wood.

Ch 7 CP 2

a) pfinal = pinitial = (0.005 kg)(500 m/s)pfinal = (Mbullet + Mwood)v = 2.5 kg m/s

v = (2.5 kg m/s)/(1.205 kg) = 2.07 m/s

9/14/2016 Physics 214 Fall 2016 32

Car travels 18 m/s and hits concrete wall. Mdriver = 90 kg.a) Find change in momentum of driver.b) What impulse produces this change in momentum?c) Explain difference between wearing and not wearing a

seat belt.

a) When driver comes to a stop his p = 0.p = 0 – (18 m/s)(90 kg) = -1620 kg m/s

b) Impulse = p = -1620 kg m/s

c) Impulse = FtWith seat belt: t is large and F is spread over torso of driverWithout seat belt: t is small. This makes F much larger (F = Impulse/t).

Ch 7 CP 4

v

p