A small heavy object of mass 10 kg travels the path ABCD which is shown in Fig. 4. ABCD is in a vertical plane; CD and AEF are horizontal. The sections of the path AB and CD are smooth but section BC is rough.
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\caption{Fig. 4}
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You should assume that
- the object does not leave the path when travelling along ABCD and does not lose energy when changing direction
- there is no air resistance.
Initially, the object is projected from A at a speed of \(16.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) up the slope.
(i) Show that the object gets beyond B .
The section of the path BC produces a constant resistance of 14 N to the motion of the object.
(ii) Using an energy method, find the velocity of the object at D .
At D , the object leaves the path and bounces on the smooth horizontal ground between E and F , shown in Fig. 4. The coefficient of restitution in the collision of the object with the ground is \(\frac { 1 } { 2 }\).
(iii) Calculate the greatest height above the ground reached by the object after its first bounce.