This problem has two parts to answer. Therefore, the question for each of the parts, and additional info, will be typed in "Description".

Question

A farmer is using a rope and pulley to lift a bucket of water from the bottom of a well. The farmer uses a force F₁ = 45.5 N to pull the bucket of water upwards at a constant speed. The bucket, when empty, has a mass of m_b = 1.3 kg.

Part 1) Calculate the mass of the water in the bucket, m_w in kg.

Part 2) Calculate the volume of the water in the bucket, V_w in cm³. Assume the density of the water, p_w, is 1.00 g/cm³.

Answer 1

Part 1)

Key point

The farmer uses a force F₁ = 45.5 N to pull the bucket of water upwards at a constant speed.

Constant speed mean no acceleration which, in turn, means the net force on the bucket is zero. So

F_net = F₁ – (m_b + m_w)g = 0 where F₁ = 45.5 N, g = 9.8 m/s², m_b = 1.3 kg and

m_w = the mass of the water in the bucket—the quantity you are trying to solve for.

F₁ – (m_b + m_w)g = 0 means F₁ = (m_b + m_w)g. Dividing both sides by g gives

F₁/g = m_b + m_w

We solve for m_w by subtracting m_b from both sides: m_w = F₁/g – m_b

Plugging in numbers

m_w = 45.5/9.8 – 1.3 = 3.34 kg

Part 2)

Since V_w × ρ_w = m this means that V_w = m/ρ_w

ρ_w = 1.00 g/cm³, m_w = 3.34 kg × 1000 g/kg = 3340 g

So V_w = (3340 g) / (1.00 g/cm³) = 3340 cm³