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 . If the total mass of the bucket with water and counterweight is 15.5 kg , what is the mass of the counter-weight?

Answer 1

m_b = mass of bucket = m

m_c = mass of counter-weight = 15.5 - m

h_b = height gained by the bucket = 1.50 m

h_c = height dropped by counterweight = 1.50 m

v = speed of both bucket and counterweight = 3 m/s

Using conservation of energy

Potential energy lost by counterweight = kinetic energy gained by counterweight + kinetic energy gained by bucket + potential energy gained by bucket

m_c g h_c = (0.5) m_c v² + (0.5) m_b v² + m_b g h_b

(15.5 - m) (9.8) (1.50) = (0.5) (15.5 - m) (3)² + (0.5) m (3)² + m (9.8) (1.50)

m = 5.4 kg

So

m_b = m = 5.4 kg

m_c = 15.5 - m = 15.5 - 5.4 = 10.1 kg