AS and A Level PhysicsOriginal material © Cambridge University Press 20101
1A body moving with speedv collides elastically with another body travelling in
the opposite direction with speed.
Which rowin the table below correctly gives the relative velocity of approach and the relative velocity of separation of the two bodies? [1]
A / /
B / /
C / /
D / /
2A body of mass m travels with a velocity 3v and collides with another particle of mass 2m which is initially stationary. After the collision, the two particles move with the same velocity.
Which row in the table gives the final velocity of the two particles and the loss in kinetic energy during the collision? [1]
A / v / mv2
B / v / 3mv2
C / 1.5 v / mv2
D / 1.5 v / 3mv2
3In an inelastic collision which quantities are conserved?[1]
Atotal kinetic energy and total momentum but not total energy
Btotal kinetic energy and total energy but not total momentum
Ctotal momentum and total energy but not total kinetic energy
Dtotal kinetic energy, total momentum and total energy
4A particle has momentum p1 at time t1 and momentum p2 at time t2.
What is the average force acting on the particle between t1 and t2?[1]
A
B
C0.5
D0.5
5What is a correct statement of the principle of conservation of momentum?[1]
Ain an inelastic collision the total kinetic energy and momentum are constant
Bin any collision the total momentum of an isolated system is constant
Cin any isolated system the force on a body equals the rate of change of momentum
Dmomentum is constant when mass and velocity are constant
6A bumper-car collides at right angles with a metal barrier and rebounds at the same speed.
A student suggests that the change in momentum of the car is zero.
Explain why the student is wrong.[2]
7Each diagram shows a 2.0 kg object before and after a collision.
Calculate the change in momentum of the object in each case.
a
[2]
b
[2]
c
[2]
8A cannon of mass850 kg fires a 20 kg shell at a velocity of 180 m s−1.
aCalculate the final momentum of the shell.[2]
bWhat is the magnitude of the momentum of the cannon immediately after the shell
is fired? (You may assume that the cannon is initially at rest.)[2]
cCalculate the recoil velocity V of the cannon.[3]
9A car of mass 900 kg travelling at a velocity of 28 m s−1 makes a head-on collision with a stationary van of mass 1500 kg. The car and the van get tangled together.
aCalculate the combined speed of the tangled vehicles immediately after the collision.[4]
bCalculate the initial kinetic energy of the car and the final kinetic energy of thetangled
car and van immediately after the collision.[3]
cUse your answer to b to explain whether the collision is elastic or inelastic.[1]
10The diagram below shows the initial state of two trolleys A and B before colliding and the
final state immediately after the collision.
Calculate the final velocity v of trolley B.[4]
11The diagram shows two toy trains T and R held in place on a level track against the force exerted by a compressed spring.
When the trains are released, R moves to the right at a speed of 3.8 m s−1. The spring takes 0.25 s to uncoilto itsnatural length.
aCalculate the velocity of train T.[4]
bCalculate the average force exerted by the spring on each train.[4]
12A ball of mass 210 g moving at a speed of 23 m s−1hits a wall at right angles and rebounds
at the same speed. The ball is in contact with the wall for 0.31 s.
aCalculate the change in momentum of the ball.[2]
bIs the momentum of the ball conserved? Explain your answer.[2]
cCalculate the magnitude of the average force acting on the ball.[3]
13The diagram below shows the initial state of two identical balls A and B before collision and the final state immediately after the collision.
The mass of each ball is 1.2 kg.
Before the collision, the velocity of A is 3.0 m s−1 and B is stationary.
A makes an oblique collision with B.
After the collision, A moves off at an angle of 30° to its original direction and has a velocity
of 2.6 m s−1. B is deflected at an angle with a velocity of 1.5 m s−1.
aExplain why the final momentum of the system in a direction at right angles to the initial
velocity of A is zero. Hence determine the angle .[3]
bShow that the total momentum of the system is conserved.[3]
Total: Score: %
6 Marking scheme: Worksheet (AS)AS and A Level PhysicsOriginal material © Cambridge University Press 20101
6 Worksheet (AS)
1D[1]
2B[1]
3C[1]
4B[1]
5B[1]
6Momentum is a vector quantity – it has both direction and magnitude.[1]
If the initial momentum of the car is p, then its final momentum must be –p(see diagram).
Change in momentum, Δp final momentum – initial momentum
Δp –p – p –2p (the change is not zero)[1]
7aΔp(2.08.0) – (2.0 4.0)[1]
Δp8.0kgms–1[1]
bΔp(2.0–4.0) – (2.0 3.0)[1]
Δp–14kgms–1[1]
cΔp(2.08.0) – (2.0–5.0)[1]
Δp26kgms–1[1]
8ap mv 20 180[1]
p 3.6103kgms–1 [1]
bThe momentum is conserved in this explosion. The momentum of the cannon is equal in magnitude but opposite in direction to that of the shell. [1]
Momentum of the cannon 3.6103kgms–1[1]
cUsing the answer from b, we have:
850 V 3.6 103[1]
V [1]
V 4.2 m s–1[1]
9ainitial momentum final momentum[1]
900 28 (1500 900) V (V combined velocity) [1]
[1]
V 10.5 m s−1 11 m s−1 [1]
bkinetic energy mv2[1]
initial kinetic energy 900 282 3.53 105 J 3.5 105 J[1]
final kinetic energy 2400 10.52 1.32 105 J 1.3 105 J[1]
cThe collision is inelastic because there is a decrease in the kinetic energy of the system.
Some of the initial kinetic energy is transformed to other forms, such as heat.[1]
10initial momentum final momentum[1]
(1.24.0)(0.80–2.5)(1.21.0)(0.80v)[1]
2.80 1.20 0.80v
v [1]
v 2.0 ms–1to the right[1]
11aInitial momentum final momentum[1]
Moving towards the right is taken as the ‘positive’ direction.
0(0.5003.8)(0.310v) (v is the velocity of T) [1]
v – (the minus sign means that T moves to the left) [1]
v –6.13ms–1 –6.1ms–1 [1]
bF [1]
Δp 0.5003.81.9kgms–1, Δt 0.25 s [1]
F [1]
F 7.6 N [1]
12aΔpmΔv 0.210 (–23 – 23) (original direction taken as ‘positive’)[1]
Δp –9.66kgms–1 –9.7kgms–1[1]
(The minus implies that the force exerted by the wall on the ball is in the opposite direction
to its initial direction of travel.)
bThe momentum of the ball itself is not conserved.[1]
The total momentum of the wall and the ball is conserved. The wall gains momentum equal
to 9.7kgms–1 but because it is massive its velocity is negligible.[1]
cF [1]
Δp –9.66kgms–1, Δt 0.31 s
F (magnitude only)[1]
F 31 N[1]
13aMomentum is a vector quantity and is conserved.
It has no component at right angles (p cos 90° 0), hence momentum in a direction at right angles to the initial momentum must be zero. [1]
Hence, 2.6 sin 30° 1.5 sin [1]
sin−1 60° [1]
bInitial momentum 1.2 3.0 3.6 kg m s−1 in the direction of A’s initial velocity.[1]
Momentum can be added vectorially.
The angle between the final velocities (and hence momentum) of A and B is 90°.[1]
The final momentum p is the vector sum of the momentum of A and the momentum of B.
final momentum p kg m s−1[1]
The initial momentum and the final momentum are the same.
OR
Initial momentum 1.2 3.0 3.6 kg m s−1 in the direction of A’s initial velocity.[1]
final momentum sum of momentum components[1]
final momentum parallel to A’s initial velocity (1.2 2.6) cos 30° (1.2 1.5) cos 60°
3.6 kg m s−1[1]
The initial momentum and the final momentum are the same. (From part a, the components of momentum at right angles to A’s initial velocity are zero.)
AS and A Level PhysicsOriginal material © Cambridge University Press 20101