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Chapter 6: Problem 77

You have decided to move a refrigerator (mass \(=81.3 \mathrm{~kg}\), including all the contents) to the other side of the room. You slide it across the floor on a straight path of length \(6.35 \mathrm{~m}\), and the coefficient of kinetic friction between floor and fridge is \(0.437 .\) Happy about your accomplishment, you leave the apartment. Your roommate comes home, wonders why the fridge is on the other side of the room, picks it up (you have a strong roommate!), carries it back to where it was originally, and puts it down. How much net mechanical work have the two of you done together?

Short Answer

Expert verified
Answer: The net mechanical work done by both the person and the roommate together is \(7264.29 \mathrm{~J}\).

Step by step solution

01

Identify the known values

We know the following values: - Mass of the refrigerator: \(m = 81.3 \mathrm{~kg}\) - Length of the path: \(d = 6.35 \mathrm{~m}\) - Coefficient of kinetic friction: \(\mu_k = 0.437\)
02

Calculate the force of friction

To calculate the force of friction, we first need to determine the gravitational force acting on the fridge. This is given by \(F_g = m \times g\) where \(g\) is the gravitational acceleration, which is approximately \(9.8 \mathrm{~m/s^2}\). So, \(F_g = 81.3 \mathrm{~kg} \times 9.8 \mathrm{~m/s^2} = 796.74 \mathrm{~N}\) The force of friction is given by \(F_f = \mu_k \times F_g\) So, \(F_f = 0.437 \times 796.74 \mathrm{~N} = 347.73 \mathrm{~N}\)
03

Calculate the work done while sliding the fridge

The work done against friction in sliding the fridge is given by \(W_1 = F_f \times d\) So, \(W_1 = 347.73 \mathrm{~N} \times 6.35 \mathrm{~m} = 2206.49 \mathrm{~J}\) (Joules)
04

Calculate the work done while lifting and carrying the fridge back

The work done against gravity in lifting the fridge is given by \(W_2 = F_g \times d\) So, \(W_2 = 796.74 \mathrm{~N} \times 6.35 \mathrm{~m} = 5057.80 \mathrm{~J}\) (Joules)
05

Calculate the net mechanical work

The net mechanical work done by both the person and the roommate is the sum of the work done by each of them: \(W_{net} = W_1 + W_2\) So, \(W_{net} = 2206.49 \mathrm{~J} + 5057.80 \mathrm{~J} = 7264.29 \mathrm{~J}\) (Joules) The net mechanical work done by both the person and the roommate together is \(7264.29 \mathrm{~J}\).

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