I\'m fine with part c) but not part d). You need the information in part c) to a

Question

I'm fine with part c) but not part d). You need the information in part c) to answer part d) I think.

c) Calculate the time taken by a sphere of mass 1 kg and radius 10 cm to roll, without slipping, down an inclined plane of slope 30°, if the distance it rolls, measured along the plane, is 1 m 17 marks d) The experiment is repeated, except that a horizontal axle is bored through the centre of the sphere. A light inextensible rope is fixed to the axle and draped over a massless pulley, as shown in the figure below. A mass of 300 g is attached to the other end of the rope. Find the time that the sphere will now take to roll 1 m down the slope 8 marks) 300 ikg 30

Explanation / Answer

(C) Fnet = m a

then m g sin30 - f = m a

and net torque = I alpha and alpha = a / r

f r = (2 m r^2 / 5)(a / r)

f = 0.4 m a

putting in previous equation,

0.5m g - 0.4 m a = m a

a = 0.5g/1.4  

Applying d = v0 t + a t^2 / 2

1 = 0 + (0.5 x 9.8 / 1.4) (t^2)/2

t = 0.756 sec ........Ans

(d) now Fnet = m a

1 g sin30 - 0.300 g - f = (1 + 0.3)a

0.2g - f = 1.3 a .... (i)

f r = (2 m r^2 / 5)(a / r)

f = 0.4 m a

0.2g - 0.4 m a = 1.3 m a

a = g / 8.5

1 = (9.8 / 8.5) t^2 / 2

t = 1.32 sec

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