Linear Momentum
A truck of mass 1200 kg is moving with speed of 7 ms – 1 when it collides with a second truck
of mass 1600 kg which is stationary. If the two trucks are automatically coupled together at
impact, with what speed do they move on together.
Answer: 3 ms – 1.
2. A bullet of mass 0.04 kg travelling horizontally at 100 ms – 1 hits a stationary block of wood of
mass 8kg, passes through it and emerges horizontally with speed of 40 ms – 1. If the block is
free to move on a smooth horizontal plane find the speed with which it is moving after the
bullet has passed through it.
Answer: 0.3 ms – 1.
3. Particle P has mass 3 kg and particle Q has mass 2 kg. The particles are moving in opposite
directions on a smooth horizontal plane when they collide directly. Immediately before the
collision, P has speed 3 ms–1 and Q has speed 2 ms–1. Immediately after the collision, both
particles move in the same direction and the difference in their speeds is 1 ms–1. Find the speed
of each particle after the collision.
Answer: vP = 0.6 m ms–1; vQ = 1.6 ms–1.
4. A particle P of mass 1.5 kg is moving along a straight horizontal line with speed 3 ms–1.
Another particle Q of mass 2.5 kg is moving, in the opposite direction, along the same straight
line with speed 4 ms–1. The particles collide. Immediately after the collision the direction of
motion of P is reversed and its speed is 2.5 ms–1.
(a) Calculate the speed of Q immediately after the impact.
(b) State whether or not the direction of motion of Q is changed by the collision.
1.
Answer: (a) 0.7 ms – 1 (b) Direction of Q unchanged.
5.
Two particles A and B have mass 0.4 kg and 0.3 kg respectively. They are moving in opposite
directions on a smooth horizontal table and collide directly. Immediately before the collision,
the speed of A is 6 ms – 1 and the speed of B is 2 ms – 1 . As a result of the collision, the
direction of motion of B is reversed and its speed immediately after the collision is 3 ms – 1.
Find the speed of A immediately after the collision, stating clearly whether the direction of
motion of A is changed by the collision,
Answer: 2.25 ms– 1.
6. Two small steel balls A and B have mass 0.6 kg and 0.2 kg respectively. They are moving
towards each other in opposite directions on a smooth horizontal table when they collide
directly. Immediately before the collision, the speed of A is 8 ms–1 and the speed of B is 2 ms–1.
Immediately after the A collision, the direction of motion of A is unchanged and the speed of B
is twice the speed of A. Find the speed of A immediately after the collision. Answer:4.4 ms– 1.
7. Two particles P and Q have masses 4m and m respectively. The particles are moving towards
each other on a smooth horizontal plane and collide directly. The speeds of P and Q
immediately before the collision are 2u and 5u respectively. Immediately after the collision, the
speed of P is 0.5 u and its direction of motion is reversed. Find the speed and direction of
motion of Q after the collision.
Answer: 5u.
8. Particle P of mass m and particle Q of mass km are moving in opposite directions on a smooth
horizontal plane when they collide directly. Immediately before the collision the speed of P is
5u and the speed of Q is u. Immediately after the collision the speed of each particle is halved
and the direction of motion of each particle is reversed. Find the value of k. Answer: k = 5.
9. Two particles A and B are moving on a smooth horizontal plane. The mass of A is km, where
2 < k < 3 , and the mass of B is m. The particles are moving along the same straight line, but in
opposite directions, and they collide directly. Immediately before they collide the speed of A is
2u and the speed of B is 4u. As a result of the collision the speed of is halved and its direction
of motion is reversed. Find, in terms of k and u, the speed of B immediately after the collision.
State whether the direction of motion of B changes as a result of the collision, explaining your
answer.
Answer: u(3k − 4); Direction of B reversed.
10. Particle P has mass m kg and particle Q has mass 3m kg. The particles are moving in opposite
directions along a smooth horizontal plane when they collide directly. Immediately before the
collision P has speed 4u ms– 1 and Q has speed km ms– 1 , where k is a constant. As a result of
the collision the direction of motion of each particle is reversed and the speed of each particle
is halved. Find the value of k.
Answer: k = 4/3.
11. A bullet of mass m fired horizontally with speed 2u into a stationary block of wood of mass
50m, which is free to move horizontally. Find the velocity of the block if
(a) the block goes right through it and emerges with speed u,
1
2
u ; (b)
u.
(b) The bullet becomes embedded in the block.
Answer: (a)
50
50
12. Three small smooth spheres A, B and C of equal radii and of masses 4 kg, 2 kg and 3 kg
respectively, lie in that order in a straight line on a smooth horizontal plane. Initially, B and C
are at rest and A is moving towards B with speed 6 m s–1. After the collison with B, sphere A
continues to move in the same direction but with speed 2 m s–1.
(a) Find the speed of B after this collison.
Sphere B collides with C. In this collison these two spheres coalesce to form an object D.
(b) Find the speed of D after this collision
(c) Show that the total loss of kinetic energy in the system due to the two collisions is 38.4 J.
Answer: (a) 8 ms – 1 (b) 3.2 ms – 1.