1 Fig. 1.1 shows block A of mass 2.5 kg which has been placed on a long, uniformly rough slope inclined at an angle \(\alpha\) to the horizontal, where \(\cos \alpha = 0.8\). The coefficient of friction between A and the slope is 0.85 .
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\caption{Fig. 1.1}
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\caption{Fig. 1.2}
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- Calculate the maximum possible frictional force between A and the slope.
Show that A will remain at rest.
With A still at rest, block B of mass 1.5 kg is projected down the slope, as shown in Fig. 1.2. B has a speed of \(16 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when it collides with A . In this collision the coefficient of restitution is 0.4 , the impulses are parallel to the slope and linear momentum parallel to the slope is conserved.
- Show that the velocity of A immediately after the collision is \(8.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) down the slope.
Find the velocity of B immediately after the collision.
- Calculate the impulse on B in the collision.
The blocks do not collide again.
- For what length of time after the collision does A slide before it comes to rest?