A bowling ball and ping-pong ball are rolling towards you with the same momentum. Which ball is moving toward you with

the greater speed?

AA) the bowling ball) the bowling ball

BB) the ping pong ball) the ping pong ball

CC) same speed for both) same speed for both

Even the lightest bowling ball (a 6-pounder) is 1000 heavier than a ping pong ball (~2.7 oz).

The ping ball would have to move ~1000 times faster!

A bowling ball and ping-pong

ball are rolling towards you with the same momentum. If you exert the same force in

stopping each, which takes a longer time to bring to rest?

AA) the bowling ball) the bowling ball

BB) the ping pong ball) the ping pong ball

CC) same time for both) same time for both

for which is the

stopping distance greater?

stopping each, which takes a longer time to bring to rest?

v v = 0

v = 0

If a cue ball moving with velocity v strikes a stationary

billiard ball head-on and comes to an abrupt halt,

v

its target ball moves off with the same velocity v.

During their brief contact

Force of red Force of billiard ball = cue ball on on cue ball billiard ball

stopping cue ball

Notice: mv + 0 = 0 + mv

launching target ball

During their brief contact

FA pushes B = FB pushes A

FAB t = FBA t over the same time!

)(AAAABBBB

vmvmvmvm

Here I use:vB to represent B’s initial velocity v0

and v'B to represent B’s final velocity.

BBAABBAAvmvmvmvm

The total momentum remains unchanged!

We say: Momentum is conserved.

A fast moving car traveling with a speed v rear-ends an identical model (and total mass) car idling in neutral

at the intersection. They lock bumpers on impact and move forward at

A) 0 (both stop).B) v/4C) v/2D) v

v

A heavy truck and light car both traveling at the speed limit v, have

a head-on collision. If they lock bumpers on impact they skid together to the

A) rightB) left

Under what conditions would they stop dead?

A heavy truck and light car have a head-on collision bringing them to a sudden stop. Which vehicle experienced

the greater force of impact?

the greater impulse?

the greater change in momentum?

the greater acceleration?

A) the truckB) the carC) both the same

A 100 kg astronaut at rest catches a 50 kg meteor moving toward him at 9 m/sec. If the astronaut managesto hold onto the meteor after catching it, what speed does he pick up?

A) 3 m/secB) 4.5 m/secC) 9 m/secD) 15 m/secE) 18 m/secF) some other speed

(100 kg0)+(50 kg9m/s) = (150kg)v' v' =450 kg·m/s 150kg

For these two vehicles to be stopped dead in their tracks by a collision at this intersection

A) They must have equal massB) They must have equal speedC) both A and BD) is IMPOSSIBLE

A

B

C

Car A has a mass of 900 kg and is travelling east at a speed of 10 m/sec. Car B has a mass of 600 kg and is travelling north at a speed of 20 m/sec. The two cars collide, and lock bumpers. Neglecting friction which arrow best represents the direction the combined wreck travels?

900 kg10 m/sec

600 kg20 m/sec

A

B

C

Car A has a mass of 900 kg and is travelling east at a speed of10 m/sec. Car B has a mass of 500 kg and is travelling north at a speed of 25 m/sec. The two cars collide and stick together.Neglecting friction Which of the arrows best represents the direction the combined wreck travels?

The answer is (A). Momentum is conserved, so the total momentum before the collision must equal the total momentum after. But momentum is a vector, so we have to add the vector arrows (by sliding them and placing them head to tail). The momentum of car A is mass velocity = 9000 kg m/s in the direction of east. The momentum of car B is mass velocity = 12000 kg m/s north. Draw these vectors, making sure to make the lengths proportional to the momenta.

900 kg10 m/sec

600 kg20 m/sec

mv0

mvf

A projectile with initial speed v0 scatters off a target (as shown) with final speed vf.

The direction its target is sent recoiling is best represented by

A

T

B CD

E

G F

mv0

mvf

A projectile with initial speed v0 scatters off a target (as shown) with final speed vf.

The sum of the final momentum (the scattered projectile and the recoilingtarget) must be the same as the initialmomentum of the projectile!

F

So the bowling ball is not moving very fast, while the ping pong ball must be moving at a pretty high speed.

But we’re told both have the same momentum! To stop either one means to remove its momentum completely.All it has (mv) to 0. So both must undergo the exact same loss in momentum. The stopping time can be figured out from the momentum change needed: )(mvFt

same for each

t must be the same for each!

The bowling ball reaches you will a small speed, v, which you slow to zero. During those t seconds, it travels with an average speed v/2, moving a distance(v/2)t before stopping. In the same amount of time, the ping pong ball travels much farther: (V/2)t.

v V

Or we can note that stopping distance can be directly computed using:

vmvmvFd 212

21

same for each

bigger vneeds

bigger d

CC) same time for both) same time for both

Question 2

BB) the ping pong ball) the ping pong ballQuestion 3

SOME ANSWERS

BB) the ping pong ball) the ping pong ballQuestion 1

Even the lightest bowling ball (a 6-pounder) is 1000 heavier than a ping pong ball (~2.7 oz).

The ping ball would have to move ~1000 times faster!

C) v/2Question 4

SOME MORE ANSWERS

22112211'' vmvmvmvm

v2=0

and since they lock bumpers and

move togetherv’1=v’2

')(2111

vmmvm and since m1 = m2 we don’t need to distinguish them by different labels.

'2')( mvvmmmv '2mvmv 2/' vv

A) rightQuestion 5

• Since forces are equal and opposite, both experience the same force.• Since both experience the same force in the same time, they both receive the same impulse.• Since they both have the same impulse, they both must undergo the same change in momentum.• Since they both experience the same force, the less massive car has a greater acceleration, since a = F/m.

Question 6

A) 3 m/secQuestion 7 (100 kg0)+(50 kg9m/s) = (150kg)v'

v' =450 kg·m/s 150kg

D) is IMPOSSIBLEQuestion 8

AQuestion 9

Momentum is conserved, so the total momentum before the collision must equal the total momentum after. But

momentum is a vector - we have to add the vector arrows (by sliding them so they meet head to tail). The momentum of car A is mass velocity = 9000 kg m/s EAST.The momentum of car B is mass velocity = 12000 kg m/s NORTH. Just try drawing these vectors, making sure their lengths are proportional to the momenta.

FF

Question 10

mvf

The question becomes:

plus WHAT? =mv0