A firm bills at the rate of $1.00 per 125 J of work. It bills you $45.00 for carrying a sofa up some stairs. Their workers moved the sofa up 3 flights of stairs, with each flight being 4.50 meters high. What is the mass of the sofa?

The mass of the sofa is 42.5 kg

Explanation:

Hi there!

Since the firm bills you $45.00 for carrying the sofa and it bills $1.00 per 125 J of work, the work done by the workers was (125 J · 45) 5625 J.

The work done by the workers is equal to the change in potential energy (PE) of the sofa:

W = ΔPE

W = m · g · h2 - m · g · h1

Where:

W = work.

m = mass of the sofa.

g = acceleration due to gravity (9.81 m/s²)

h2 = final height.

h1 = initial height.

In this case, h1 = 0, then:

W = m · g · h

The height is (3 · 4.50 m) 13.5 m. So, the mass of the sofa can be calculated:

W = m · g · h

5626 J = m · 9.81 m/s² · 13.5 m

5625 J / (9.81 m/s² · 13.5 m) = m

m = 42.5 kg

The mass of the sofa is 42.5 kg