Answer:
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
