A bullet of mass 0.04 kg is fired into a fixed uniform rectangular block along a line through the centres of opposite parallel faces, as shown in Fig. 2.1.
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The bullet enters the block at \(50 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and comes to rest after travelling 0.2 m into the block.
Calculate the resistive force on the bullet, assuming that this force is constant.
Another bullet of the same mass is fired, as before, with the same speed into a similar block of mass 3.96 kg . The block is initially at rest and is free to slide on a smooth horizontal plane.
By considering linear momentum, find the speed of the block with the bullet embedded in it and at rest relative to the block.
By considering mechanical energy, find the distance the bullet penetrates the block, given the resistance of the block to the motion of the bullet is the same as in part (i).
Fig. 2.2 shows a block of mass 6 kg on a uniformly rough plane that is inclined at \(30 ^ { \circ }\) to the horizontal.
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A string with a constant tension of 91.5 N parallel to the plane pulls the block up a line of greatest slope. The speed of the block increases from \(1 \mathrm {~ms} ^ { - 1 }\) to \(7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) over a distance of 8 m .