This is a Mechanics Question,?

Question

A 15 kg mass hangs in the loop of a light inextensible cable, one end of the cable being fixed and the other wound round a wheel of radius 0.3m and moment of Inertia 0.9 kgm^2 so that the lengths of the cable are vertical. The mass is released from rest and falls, turning the wheel (take g=9.81). Neglecting friction between the mass and the loop of the cable and between the wheel and its bearings, find:

a relationship between the downward velocity of the mass, v, and the angular velocity of the wheel, w.

the speed of the mass when it has fallen a distance of 2m

the number of turns of the wheel before it reaches a rotation rate of 300rpm

Answer 1

m = 15, r = 0.3 , I = 0.9
conserve torque to find a
mar = mgr - Iα = mgr - Ia/r
so
a = mgr/(mr + I/r)............(1)
then

first
v = wr.............(2)

second
v^2 = 2ad.................(3)
substitute (1) and d=2 in (3) to find v

third
d = k2πr ................(4)
where k = # of turns
w = 300rpm = 300 * 2π / 60 = 10π s^-1
substitute (2) and (4) and w = 10π in (3) to find k

answers
a = 5.9m/s^2
(second) .........v = 4.9m/s
(third) ..............k = 4 turns

the end
.

Answer 2

This sounds like a homework question. Did you try looking in the book?

Answer 3

Try using conservation of energy.

Answer 4

sorry i don't know