A battering-ram consists of a wooden beam fixed to a trolley. The battering-ram runs along horizontal ground and collides directly with a vertical wall, as shown in Fig. 1.1. The batteringram has a mass of 4000 kg .
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Initially the battering-ram is at rest. Some men push it for 8 seconds and let go just as it is about to hit the wall. While the battering-ram is being pushed, the constant overall force on it in the direction of its motion is 1500 N .
At what speed does the battering-ram hit the wall?
The battering-ram hits a loose stone block of mass 500 kg in the wall. Linear momentum is conserved and the coefficient of restitution in the impact is 0.2 .
Calculate the speeds of the stone block and of the battering-ram immediately after the impact.
Calculate the energy lost in the impact.
Small objects A and B are sliding on smooth, horizontal ice. Object A has mass 4 kg and speed \(18 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the \(\mathbf { i }\) direction. B has mass 8 kg and speed \(9 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the direction shown in Fig. 1.2, where \(\mathbf { i }\) and \(\mathbf { j }\) are the standard unit vectors.
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Write down the linear momentum of A and show that the linear momentum of B is \(( 36 \mathbf { i } + 36 \sqrt { 3 } \mathbf { j } )\) Ns.
After the objects meet they stick together (coalesce) and move with a common velocity of \(( u \mathbf { i } + v \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).
Calculate \(u\) and \(v\).
Find the angle between the direction of motion of the combined object and the \(\mathbf { i }\) direction. Make your method clear.