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1 Momentum Worksheet with Answers

MOMENTUM Worksheet
Section 1
Calculate the momentum of the following.
(a) A 110 kg rugby player is running at 3.5 ms-1.
(b) A 7.5 g bullet is travelling at 200 ms-1.
A boy throws a 0.2 kg wooden ball at a coconut of mass 0.4 kg which is balanced on the top of
a stick. Just before the ball hits the coconut it is travelling horizontally at 25 ms-1.
(a) Calculate the momentum of the ball before the collision.
(b) If the collision causes the ball to stop moving, calculate the speed of the coconut.
Two identical billiard balls are rolling towards each other. Ball A is travelling at 1.2 ms-1 and
ball B is travelling at 0.8 ms-1 as shown below. The mass of each ball is 80 g.
(a) What is the initial total momentum of the balls?
(b) After the collision, ball A is travelling to the right at 0.15 ms-1. Calculate the speed and
direction of ball B?
(c) Calculate the kinetic energy of the balls before the collision.
(d) Calculate the kinetic energy of the balls after the collision. Is it an elastic collision?
A child’s toy consists of two pieces of plastic clipped together in such a way that they compress
a spring between them. When touched, the toy “explodes” and the two pieces of plastic fly
apart to give someone a fright.
(a) Would momentum be conserved in this “explosion”?
(b) Would the “explosion” be elastic?
(c) If the masses of the two pieces were not identical, comment on the speed of the pieces as
they “exploded” apart.
A 12 kg dog is on a leash and the other end of his leash is tied to a stationary supermarket
trolley. The dog sees another dog and runs away from the trolley at 12ms-1. The trolley has a
mass of 9 kg. When the leash goes tight the trolley moves in the direction of the dog.
(a) What is the momentum of the dog as it runs away from the trolley?
(b) What is the speed of the trolley and the dog just after the leash tightens?
A 1.3 kg magnet is slid across a layer of ice at 3.5 ms-1 and collides with a 3.2 kg steel cube.
The two objects stick together and continue to slide in the original direction of the magnet’s
(a) Determine the original momentum of the magnet.
(b) Determine the final speed of the magnet and steel cube.
(c) Is the collision elastic?
A gun of mass 1.8 kg fires a bullet of mass 0.025 kg. The velocity of the bullet as it leaves the
gun is 200ms-1. Calculate the recoil velocity of the gun.
Section 2
Two students start to push their car, which has broken down, along the road. They push with a
combined force of 2000 N for 20 seconds and then give up. (Assume no loss of energy
through friction.)
(a) Calculate the change in momentum of the car.
(b) If the car was stationery to begin with, and has a mass of 1,100 kg, calculate the speed of
the car when the students stop pushing.
Tom and Andrew are playing in an ice hockey match. Tom is 80 kg and Andrew is 90 kg.
During the game Tom is skating at 4ms-1 and bangs into Andrew who is stationary. After the
collision they move together for a few seconds.
(a) What is Tom’s momentum?
(b) What is the speed of Tom and Andrew after the collision?
(c) If the collision lasts for 0.6 second, calculate the force that Tom exerts on Andrew.
(d) What force did Andrew exert on Tom?
When a car travelling at 50 kmh-1 crashes into a solid concrete pole that does not move in the
collision, the damage to passengers from the collision forces is greater than if the car hit a pile
of old tires and came to a stop over a few meters.
Using the principles of momentum and impulse explain why this is so.
Section 3
(a) p = mv = 110 x 3.5 = 385 kgms-1
(b) p = mv = 0.0075 x 200 = 1.5 kgms-1
(a) p = mv = 0.2 x 25 = 5 kgms-1
(b) p (coconut) = p (ball) = 5 kgms-1  v = 5/0.4 = 12.5 ms-1
(a) p (total) = p (A) = p (B) = 0.08x 1.2 - 0.08x 0.8
= 0.032 kgms-1 to the right
(b) p (total) = p (A) = p(B) = 0.032
v (B) = (0.032- 0.012)/ 0.08 = 0.25 ms-1 to the right
(c) Ek (before) = 1/2x 0.08 x (1.2)2 + 1/2 x 0.08 x (0.8)2
= 0.083 J
(d) Ek (after) = ½ x 0.08 x (1.22 + 0.252)
= 0.0034 J So collision is not elastic.
(a) Yes
(b) No
(c) The bigger piece (more mass) would fly off more slowly than
the smaller piece.
(a) p = mv = 12 x 12 = 144 kgms-1
(b) ptot = pdog + p trolley
144 = (9 + 12)v
v = 144/21 = 6.9 ms-1
(a) p = mv = 1.3 x 3.5 = 4.6 kgms-1
(b) ptot = (1.3 + 3.2)v
v = 4.55/4.5 = 1 ms-1
(c) Ek (before) = 7.96 J
Ek (after) = 2.25 J
Not elastic.
mgunvgun = mbulletvbullet
vgun = (o.o25 x 200)/1.8 = 2.8 ms-1
Section 2
(a) p = F x t = 2000 x 20 = 40000 Ns
(b) p = 40000 = mv
v = 40000/1100 = 36 ms-1
(a) ptom = 80 x 4 = 320 kgms-1
(b) Momentum of Tom and Andrew = 320 kgms-1
320 = (80 + 90)v
v = 320/170 = 1.9 ms-1
(c) Momentum change experienced by Tom = pf - pi = (80 x 1.9) - 320
= 152 - 320 = - 168 kgms-1
F = p /t = 168/0.6 = 280 N
(d) Same as (c), ie 280 N
The car that hits the power pole loses the same amount of momentum in
coming to a stop as it does when it crashes into a pile of tires.
However the time taken to lose that momentum is different in each case.
The car will come a stop much faster when it hits the power pole.
Because F = p /t the power pole collision will exert a much greater force
on the car and its occupants than the pile of tires producing greater damage
Section 3