A large crate located on the flat roof of a building is connected with a bucket

Question

A large crate located on the flat roof of a building is connected with a bucket full of concrete by means of an unstretchable rope that passes through a pulley. The bucket, whose mass is equal to 20 Kg, hangs on the side of the building. The mass of the crate is equal to 100 Kg and can slide on the roof without any friction.

a) Compute the weights of the bucket and the crate
b) Compute the acceleration of the bucket (neglecting the effect of friction)

c) Compute the tension in the rope connecting the two objects

Explanation / Answer

Here ,

m1 = 20 Kg

m2 = 100 Kg

a) weight of the crate = m2 * g

weight of the crate = 100 * 9.8

weight of the crate = 980 N

weight of the bucket = 20 * g

weight of the bucket = 20 * 9.8

weight of the bucket = 196 N

b)

let the acceleration of the bucket is a

Using second law of motion

(m1 + m2) * a = m1 * g

(100 + 20) * a = 20 * 9.8

a = 1.633 m/s^2

the acceleration of the bucket is 1.633 m/s^2

c)

let the tension in the rope is T

Using Second law of motion for crate

T - m2 * a = 0

T = 100 * 1.633 = 0

T = 163.3 N

the tension in the rope connecting the two objects is 163.3 N

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