A-Level CAIE Mathematics AS 4.3 Momentum Question Bank

A particle B of mass 5 kg is at rest on a smooth horizontal table. A particle A of mass 2.5 kg moves on the table with a speed of $6 \mathrm{~m} \mathrm{~s}^{-1}$ and collides directly with B. In the collision the two particles coalesce.

Small smooth spheres A and B, of equal radii and of masses 5 kg and 3 kg respectively, lie on a smooth horizontal plane. Initially B is at rest and A is moving towards B with speed $8.5 \mathrm{~ms}^{-1}$. The spheres collide and after the collision A continues to move in the same direction but with a quarter of the speed of B.

Two particles P and Q, of masses 0.3 kg and 0.2 kg respectively, are at rest on a smooth horizontal plane. P is projected at a speed of $4 \mathrm{~m} \mathrm{~s}^{-1}$ directly towards Q. After P and Q collide, Q begins to move with a speed of $3 \mathrm{~m} \mathrm{~s}^{-1}$.

Particles P of mass $m \mathrm{~kg}$ and Q of mass 0.2 kg are free to move on a smooth horizontal plane. P is projected at a speed of $2 \mathrm{~ms}^{-1}$ towards Q which is stationary. After the collision P and Q move in opposite directions with speeds of $0.5 \mathrm{~m} \mathrm{~s}^{-1}$ and $1 \mathrm{~m} \mathrm{~s}^{-1}$ respectively.

Find m.

Two particles P and Q of masses 0.2 kg and 0.3 kg respectively are free to move in a horizontal straight line on a smooth horizontal plane. P is projected towards Q with speed $0.5 \mathrm{~m} \mathrm{~s}^{-1}$. At the same instant Q is projected towards P with speed $1 \mathrm{~ms}^{-1} . Q$ comes to rest in the resulting collision.

Find the speed of P after the collision.

A metal post is driven vertically into the ground by dropping a heavy object onto it from above. The mass of the object is 120 kg and the mass of the post is 40 kg (see diagram). The object hits the post with speed $8 \mathrm{~m} \mathrm{~s}^{-1}$ and remains in contact with it after the impact.

Particles P of mass 0.4 kg and Q of mass 0.5 kg are free to move on a smooth horizontal plane. P and Q are moving directly towards each other with speeds $2.5 \mathrm{~m} \mathrm{~s}^{-1}$ and $1.5 \mathrm{~m} \mathrm{~s}^{-1}$ respectively. After P and Q collide, the speed of Q is twice the speed of P.

Find the two possible values of the speed of P after the collision.

Small smooth spheres A and B, of equal radii and of masses 6 kg and 2 kg respectively, lie on a smooth horizontal plane. Initially A is moving towards B with speed $5 \mathrm{~m} \mathrm{~s}^{-1}$ and B is moving towards A with speed $3 \mathrm{~m} \mathrm{~s}^{-1}$. After the spheres collide, both A and B move in the same direction and the difference in the speeds of the spheres is $2 \mathrm{~ms}^{-1}$.

Find the loss of kinetic energy of the system due to the collision.

Two small smooth spheres A and B, of equal radii and of masses km kg and $m \mathrm{~kg}$ respectively, where k>1, are free to move on a smooth horizontal plane. A is moving towards B with speed $6 \mathrm{~ms}^{-1}$ and B is moving towards A with speed $2 \mathrm{~m} \mathrm{~s}^{-1}$. After the collision A and B coalesce and move with speed $4 \mathrm{~ms}^{-1}$.

Three particles P, Q and R, of masses $0.1 \mathrm{~kg}, 0.2 \mathrm{~kg}$ and 0.5 kg respectively, are at rest in a straight line on a smooth horizontal plane. Particle P is projected towards Q at a speed of $5 \mathrm{~m} \mathrm{~s}^{-1}$. After P and Q collide, P rebounds with speed $1 \mathrm{~ms}^{-1}$.