Question

A bucket and a counter-weight are used to lift water out of a well. The bucket and counter-weight are attached to either end of a light rope that passes over a light, frictionless pulley, with the rope hanging straight down to both. The mass of the counter-weight is greater than the mass of the bucket filled with water.

The bucket starts at the bottom of the well and the counter-weight starts at the top. The counter-weight is released from rest and starts to descend. After the counter-weight has dropped 1.50 m, its speed is 3.00 m/s.

A. If the total mass of the bucket with water and counterweight is 20.0 kg , what is the mass of the counter-weight?

B. If the total mass of the bucket with water and counterweight is 20.0 kg , what is the mass of the filled bucket?

Answer 1

A)

consider the motionof counter-weights

d = distance dropped = 1.50 m

v_o = initial velocity = 0 m/s

v_f = final velocity after dropping 1.50 m = 3 m/s

a = acceleration = ?

Using the equation

v_f² = v_o² + 2 a d

3² = 0² + 2 a (1.50)

a = 3 m/s²

M = mass of counterweight

m = mass of bucket with water

given that , M + m = 20 eq-1

acceleration of the system is given as

a = (M - m) g/(M + m)

3 = (M - m) g /(20)

M - m = 6.12 eq-2

adding eq-1 and eq-2

M + m + M - m = 20 + 6.12

2M = 26.12

M = 13.06 kg

using eq-1

M + m = 20

13.06 + m = 20

m = 6.94 kg