8 Fig. 8.1 shows a sledge of mass 40 kg . It is being pulled across a horizontal surface of deep snow by a light horizontal rope. There is a constant resistance to its motion.
The tension in the rope is 120 N .
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\caption{Fig. 8.1}
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The sledge is initially at rest. After 10 seconds its speed is \(5 \mathrm {~ms} ^ { - 1 }\).
- Show that the resistance to motion is 100 N .
When the speed of the sledge is \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the rope breaks.
The resistance to motion remains 100 N .
- Find the speed of the sledge
(A) 1.6 seconds after the rope breaks,
(B) 6 seconds after the rope breaks.
The sledge is then pushed to the bottom of a ski slope. This is a plane at an angle of \(15 ^ { \circ }\) to the horizontal.
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\caption{Fig. 8.2}
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The sledge is attached by a light rope to a winch at the top of the slope. The rope is parallel to the slope and has a constant tension of 200 N . Fig. 8.2 shows the situation when the sledge is part of the way up the slope.
The ski slope is smooth. - Show that when the sledge has moved from being at rest at the bottom of the slope to the point when its speed is \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), it has travelled a distance of 13.0 m (to 3 significant figures).
When the speed of the sledge is \(8 \mathrm {~ms} ^ { - 1 }\), this rope also breaks.
- Find the time between the rope breaking and the sledge reaching the bottom of the slope.