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Found in: Page 137

### Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271

# Question: A crate remains stationary after it has been placed on a ramp inclined at an angle with the horizontal. Which of the following statements is or are correct about the magnitude of the friction force that acts on the crate? Choose all that are true. (a) It is larger than the weight of the crate. (b) It is equal to ${\mathbit{\mu }}{\mathbf{,}}{\mathbit{n}}$. (c) It is greater than the component of the gravitational force acting down the ramp. (d) It is equal to the component of the gravitational force acting down the ramp. (e) It is less than the component of the gravitational force acting down the ramp.

The correct option is (d): It is equal to the component of the gravitational force acting down the ramp.

See the step by step solution

## Step 1: Definition of frictional force

The frictional force is the force that opposes the motion between two objects in surface contact.

The equation to calculate the frictional force is as follows:

${\mathrm{f}}_{\mathrm{k}}={\mathrm{\mu }}_{\mathrm{s}}\mathrm{n}$

Here, ${\mathrm{\mu }}_{\mathrm{s}}$ is the coefficient of the kinetic friction, and $\mathrm{n}$is the normal force.

## Step 2: Determine the correct statements

Consider the free-body diagram of the crate, placed on the ramp at an angle with the horizontal plane.

Since the crate is stationary on the ramp, the net vertical and horizontal forces are zero.

Consider the forces in the horizontal plane.

$\begin{array}{l}\sum _{}^{}{F}_{x}=0\\ mg\mathrm{sin}\theta -f=0\\ f=mg\mathrm{sin}\theta \end{array}$

The frictional force is equal to the component of the gravitational force acting downward on the ramp.

Hence, the frictional force must be equal to the component of the gravitational force acting down the ramp.