Sphere P , of mass 10 kg , and sphere Q , of mass 15 kg , move with their centres on a horizontal straight line and have no resistances to their motion. \(\mathrm { P } , \mathrm { Q }\) and the positive direction are shown in Fig. 1.1.
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Initially, P has a velocity of \(- 1.75 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and is acted on by a force of magnitude 13 N acting in the direction PQ .
After \(T\) seconds, P has a velocity of \(4.75 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and has not reached Q .
Calculate \(T\).
The force of magnitude 13 N is removed. P is still travelling at \(4.75 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when it collides directly with Q , which has a velocity of \(- 0.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
Suppose that P and Q coalesce in the collision to form a single object.
Calculate their common velocity after the collision.
Suppose instead that P and Q separate after the collision and that P has a velocity of \(1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) afterwards.
Calculate the velocity of Q after the collision and also the coefficient of restitution in the collision.
Fig. 1.2 shows a small ball projected at a speed of \(14 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(30 ^ { \circ }\) below the horizontal over smooth horizontal ground.
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The ball is initially 3.125 m above the ground. The coefficient of restitution between the ball and the ground is 0.6 .
Calculate the angle with the horizontal of the ball's trajectory immediately after the second bounce on the ground.