Answer to Question #170274 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

By definition, the frictional force that acts on the book is:

$$F_{fr} = \mu_k mg$$

where $\mu_k = 0.25, m = 1.5kg$, and $g = 9.8N/kg$ is the gravitational acceleration.

$$F_{fr} = 0.25\cdot 1.5\cdot 9.8 = 3.675N$$

In turn, the work is:

$$A = F_{fr}d$$

where $d$ is the distance travelled by the book (different in different cases).

a) In this case the total distance is double the side of the square: $d = 16m$ . Thus the work is:

$$A_a = 3.675N\cdot 16m = 58.8J$$

b) In this case the total distance is the diagonal of the square: $d =8\sqrt{2}m$. Then the work is:

$$A_b = 3.675N\cdot 8\sqrt{2}m \approx 41.6J$$

c) Again, the book covered the distacne $d = 16m$, thus the work is the same as in a):

$$A_c = 58.8J$$

d) If the force had been conservative, the works would've satisfied:

$$A_a = A_b\space (\text{the work of the potential force depends only on displacement})\\ A_c = 0 \space (\text{displacement is 0, thus the work is zero})$$

Answer. non-conservative.