A bucket of water with a mass of 2.0 kg is attached to a rope that is wound arou

Question

A bucket of water with a mass of 2.0 kg is attached to a rope that is wound around a cylinder. The cylinder has a mass of 4.0 kg and is mounted horizontally on frictionless bearings. The bucket is released from rest.

A bucket of water with a mass of 2.0 kg is attached to a rope that is wound around a cylinder. The cylinder has a mass of 4.0 kg and is mounted horizontally on frictionless bearings. The bucket is released from rest. (a) Find its speed after it has fallen through a distance of 1.10 m? (b) What is the tension in the rope? N (c) What is the acceleration of the bucket? m/s2

Explanation / Answer

Here ,

for the cyclinder , v = r*w

v is the speed of bucket

w is the angular speed of cyclinder

a)

Using conservation of energy

0.5I*w^2 + 0.5mv^2 = mgh

0.5 * 0.5*4 *r^2 * (v/r)^2 + 0.5 * 2 * v^2 = 2 * 9.8 * 1.1

solving for v

v = 3.28 m/s

the speed of bucket is 3.28 m/s

B)

Now , using third euqaiton of motion

v^2 - 0^2 = 2 * d* a

3.28^2 = 2 * 1.1 * a

a = 4.89 m/s^2

Now , let the tension in the string is T

mg - T = ma

2 * 9.8 - T = 2 * 4.89

T = 9.82 N

the tension in the rope is 9.82 N

c)

the acceleration of bucket is 4.89 m/s^2

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