Question

(a) The combined mass of a man and his bicycle is 90 kg. He cycles up...

(a) The combined mass of a man and his bicycle is 90 kg. He cycles up a hill with incline 1 : 10 at a velocity of 4 m s−1 . If his power output is 500W, find the frictional force acting assuming that it is constant.

(b) A block A of mass 5m lies on a rough inclined plane of angle α where cos(α) = 4/5 with coefficient of friction µ. It is connected via a light inextensible string, passing over a smooth fixed pulley at the top of the plane, to a vertically hanging block B of mass m

(i) Find the acceleration of the block down the plane in terms of µ

(ii) Show that the block moves down the plane provided µ < 1/2

(iii) Suppose that µ = 1/4 and the system is released from rest. Show that A and B have speed √ 10 m s−1 after moving 3 m.

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