Question

You place a book of mass 5.00 kg against a vertical wall. You apply a constant force f⃗ to the book, where f = 84.0 N and the force is at an angle of 60.0° above the horizontal (Figure 1). The coefficient of kinetic friction between the book and the wall is 0.300. What is the magnitude of the frictional force acting on the book?

1) 20.0 N
2) 40.0 N
3) 60.0 N
4) 80.0 N

Answer 1

The magnitude of the frictional force is calculated by first determining the normal force exerted on the book, which includes the horizontal component of the applied force and the book's weight, and then multiplying the normal force by the coefficient of kinetic friction.

Step-by-step explanation:

To find the magnitude of the frictional force acting on the book against the wall, you need to consider the normal force exerted on the book. Since the force you apply is at a 60° angle, only the horizontal component of this force will contribute to the normal force. Using trigonometry, the horizontal component of the applied force (Fhorizontal) is F cos(60°).

The normal force acting on the book (N) is the sum of this horizontal component and the gravitational force acting on the book, which is the book's weight (W = mg). Since the book is stationary and not sliding down, the normal force must counteract the entire weight of the book, so N = Fhorizontal + W. By substituting the given values, we get N = (84.0 N) cos(60°) + (5.00 kg)(9.80 m/s²).

Once the normal force is calculated, the kinetic friction (fk) can be found using the formula fk = μk N, where μk is the coefficient of kinetic friction. Putting all this together, the kinetic friction acting on the book is 0.300 times the normal force calculated previously.