CONSERVATION OF MOMENTUM.

• The law of conservation of momentum states that in any collision or interaction between two or more objects in an isolated system the total momentum of the system will remain constant.

• The total initial momentum will equal the total final momentum:

Σpi = Σpf

• Conservation of momentum can be extended to any number of colliding objects within an isolated system.

Use g = 9.8 m s−2 when required.

1 A white billiard ball of mass 100 g travelling at 2.0 ms−1 across a low-friction billiard table has a head-on collision with a black ball of the same mass initially at rest. The white ball stops while the black ball moves off. What is the velocity of the black ball? v = 2.0 ms-1 in the direction of white ball’s original motion

2 A girl with mass 50 kg running at 5 m s−1 jumps onto a 4 kg skateboard travelling in the same direction at 1.0 m s−1.

What is their new common velocity? v = 4.70 ms-1 in the same direction

3 A man of mass 70 kg steps forward out of a boat and onto the nearby river bank with a velocity, when he leaves the boat, of 2.5 m s−1 relative to the ground. The boat has a mass of 400 kg and was initially at rest. With what velocity relative to the ground does the boat begin to move? v = 0.44 ms-1 in the opposite direction

4 A railway car of mass 2 tonnes moving along a horizontal track at 2 m s−1 runs into a stationary train and is coupled to it. After the collision the train and car move off at a slow 0.3 m s−1. What is the mass of the train alone? m = 11,333.3 kg

5 A trolley of mass 4.0 kg and moving at 4.5 m s−1 collides with, and sticks to, a stationary trolley of mass 2.0 kg.

Their combined speed in m s−1 after the collision is: A 2.0 B 3.0 C 4.5 D 9.0 B as v = 3 ms-1

6 Superman stops a truck simply by blocking it with his outreached arm.

a Is this consistent with the law of conservation of momentum? Explain.

Only if Superman is fixed to the ground so the momentum of truck can be transferred to the ground.

b Using reasonable estimates for the initial speed and mass of the truck and Superman demonstrate what will happen. Use appropriate physics concepts.

If mass truck = 8000 kg, mass Superman = 80 kg and initial velocity truck = 20 ms-1 and Superman is still…

Assuming they stick together they will move off with a common velocity of 18.18 ms-1 in the original direction.

7 A car of mass 1100 kg has a head-on collision with a large four-wheel drive vehicle of mass 2200 kg, immediately after which both cars are stationary. The four-wheel drive vehicle was travelling at 50 km h−1 prior to the collision in an area where the speed limit was 70 km h−1. Was the car breaking the speed limit? vcar = 100 km hr-1 Yes it was speeding.

8 A 100 g apple is balanced on the head of young master Tell. William, the boy’s father, fires an arrow with a mass of 80 g at the apple. It reaches the apple with a velocity of 35 m s−1. The arrow passes right through the apple and goes on with a velocity of 25 m s−1. With what speed will the apple fly off the boy’s head (assume no friction between apple and head)?

Speed = 8.0 ms-1 ( in same direction as arrow.)

9 A space shuttle of mass 10 000 kg, initially at rest, burns 5.0 kg of fuel and oxygen in its rockets to produce exhaust gases ejected at a velocity of 6000 m s−1. Calculate the velocity that this exchange will give to the space shuttle.

v = 3 ms-1 in opposite direction to exhaust gases.

10 A small research rocket of mass 250 kg is launched vertically as part of a weather study.

It sends out 50 kg of burnt fuel and exhaust gases with a velocity of 180 m s−1 in a 2 s initial acceleration period.

a What is the velocity of the rocket after this initial acceleration? v = 40 ms-1 upwards

b What upward force does this apply to the rocket? Favg = 4500 N

c What is the net upward acceleration acting on the rocket? a = 10.2 ms-2