Answer to Question #170275 in Physics for RHYLYN

Question

You and three friends stand at the corners of a square whose sides are 8.0 m long in the middle of the gym floor, as shown below. You take your physics book and push it from one person to the other. The book has a mass of 1.5 kg, and the coefficient of kinetic friction between the book and the floor is μ_k=0.25

a. The book slides from you to Beth and then from Beth to Carlos, along the lines connecting these people. What is the work done by friction during this displacement?

b. You slide the book from you to Carlos along the diagonal of the square. What is the work done by friction during this displacement?

c. You slide the book to Kim, who then slides it back to you. What is the total work done by friction during this motion of the book?

d. Is the friction force on the book conservative or non-conservative? Explain.

Answer 1

a. The work done by friction during this displacement along two sides of the square is

$$W=\mu mg x=\mu mg(a+a)=2\mu mga,\\ W=117.6\text{ J}.$$

b. The work by friction in this displacement is

$$W=\mu mga\sqrt2=83.2\text{ J}.$$

c. In this case, as in both previous ones, the friction does work along the entire covered distance:

$$W=2\mu mga=117.6\text{ J}.$$

d. The friction force on the book is non-conservative, which means that it depends on the path taken, not initial and final position. Also, it means that the energy is remo0ved from the system and is converted into heat: people spend their muscular mechanical energy - energy of the system decreases - and dissipates into heat as a result of friction.