Direct collision, find mass

Two particles collide directly; given initial and final velocities and one mass, find the unknown mass using conservation of momentum.

5 questions · Moderate -0.9

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CAIE M1 2020 June Q1
3 marks Easy -1.2
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 \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) 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 \(m\).
Edexcel M1 2024 January Q2
6 marks Moderate -0.8
2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e59a66b8-c2ad-41fd-9959-9d21e9455c37-04_204_947_242_559} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows two particles, \(A\) and \(B\), moving in opposite directions on a smooth horizontal surface. Particle \(A\) has mass 5 kg and particle \(B\) has mass \(x \mathrm {~kg}\). The particles collide directly.
Immediately before the collision, the speed of \(A\) is \(3 \mathrm {~ms} ^ { - 1 }\) and the speed of \(B\) is \(x \mathrm {~ms} ^ { - 1 }\)
Immediately after the collision, the speed of \(A\) is \(1 \mathrm {~ms} ^ { - 1 }\) and its direction of motion is unchanged. Immediately after the collision, the speed of \(B\) is \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
  1. Find the value of \(x\).
  2. Find the magnitude of the impulse exerted on \(A\) by \(B\) in the collision.
Edexcel M1 2014 June Q1
5 marks Moderate -0.8
  1. Two small smooth balls \(A\) and \(B\) have mass 0.6 kg and 0.9 kg respectively. They are moving in a straight line towards each other in opposite directions on a smooth horizontal floor and collide directly. Immediately before the collision the speed of \(A\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of \(B\) is \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The speed of \(A\) is \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) immediately after the collision and \(B\) is brought to rest by the collision.
Find
  1. the value of \(v\),
  2. the magnitude of the impulse exerted on \(A\) by \(B\) in the collision.
Edexcel M1 2008 January Q1
6 marks Moderate -0.8
  1. Two particles \(A\) and \(B\) have masses 4 kg and \(m \mathrm {~kg}\) 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 \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of \(B\) is \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Immediately after the collision, the direction of motion of \(A\) is unchanged and the speed of \(A\) is \(1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
    1. Find the magnitude of the impulse exerted on \(A\) in the collision.
    Immediately after the collision, the speed of \(B\) is \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  2. Find the value of \(m\).
OCR M1 2006 June Q1
5 marks Moderate -0.8
1 Each of two wagons has an unloaded mass of 1200 kg . One of the wagons carries a load of mass \(m \mathrm {~kg}\) and the other wagon is unloaded. The wagons are moving towards each other on the same rails, each with speed \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), when they collide. Immediately after the collision the loaded wagon is at rest and the speed of the unloaded wagon is \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find the value of \(m\).