A rope is over a pulley wheel as shown in the diagram. Masses of M kg and 10 kg,

Question

A rope is over a pulley wheel as shown in the diagram. Masses of M kg and 10 kg, are attached to the ends of the rope as shown. The radius of the wheel is 50.0 cm and its mass is 40.0 kg. The rope does not slip as the wheel begins to rotate when the system is released from rest. When released from rest, the 10 kg mass accelerates upwards and the wheel makes 39.0 revolutions in the first ten seconds.

i)Find the angular acceleration of the wheel when the system is released. 20 kg . = 50 cm 10 kg .

ii)Calculate the magnitude of the unknown mass, M.

Explanation / Answer

Given:M=10Kg
R=50cm
m=40kg
omega=39rev
10sec=t

Let
T1 = tension of the rope supporting M
T2 = tension of the rope supporting m
m = 10 kg
I = ½(Mw)*R² = ½*40*(.50)² = 5 kgm²
= 39*2 = 245 radians
t = 10 sec

1. = 2/t² = 4.90 rad/sec²

2.
Acceleration a = *R = 2.45 m/sec²
but
b) a = g - T1/M
and
c) a = T2/m - g

Solving (a), (b) and (c) simultaneously gives me
T1 = 171.5 N
T2 = 122.5 N
and

M = 23.33 kg

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