Two model railway trucks are moving freely on a straight horizontal track when they are in a direct collision.
The trucks are P of mass 0.5 kg and Q of mass 0.75 kg . They are initially travelling in the same direction. Just before they collide P has a speed of \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and Q has a speed of \(1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), as shown in Fig. 1.1.
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Suppose that the speed of P is halved in the collision and that its direction of motion is not changed. Find the speed of Q immediately after the collision and find the coefficient of restitution.
Show that it is not possible for both the speed of P to be halved in the collision and its direction of motion to be reversed.
Both of the model trucks have flat horizontal tops. They are each travelling at the speeds they had immediately after the collision.
Part of the mass of Q is a small object of mass 0.1 kg at rest at the edge of the top of Q nearest P . The object falls off, initially with negligible velocity relative to Q .
Determine the speed of Q immediately after the object falls off it, making your reasoning clear.
Part of the mass of P is an object of mass 0.05 kg that is fired horizontally from the top of P , parallel to and in the opposite direction to the motion of P . Immediately after the object is fired, it has a speed of \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) relative to P .
Determine the speed of P immediately after the object has been fired from it.
The velocities of a small object immediately before and after an elastic collision with a horizontal plane are shown in Fig. 1.2.
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