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Q12OQ

Expert-verifiedFound in: Page 137

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 ${\mathit{\mu}}{\mathbf{,}}{\mathit{n}}$. (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.

**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.

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.

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