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#### Concept explainers

In Fig. 6-12, if the box is stationary and the angle *θ* between the horizontal and force
*F _{x};* (b) ƒ

_{s}; (c)

*F*(d) ƒ

_{N};_{s, max}? (e) If, instead, the box is sliding and

*θ*is increased, does the magnitude of the frictional force on the box increase, decrease, or remain the same?

**Figure 6-12 **Question 1.

**To find**:

Whether the following quantities increase, decrease, or remain the same when an applied force is directed downward at an angle

(a)

(b)

(c)

(d)

(e) And, whether the magnitude of the frictional force on the box increases, decreases, or remains the same if the angle θ is increased.

## Answer to Problem 1Q

**Solutions:**

(a) The value of horizontal force

(b)

(c) The value of the normal force

(d)

(e) The friction force increases when the box slides and the angle between the surface and box also increases.

### Explanation of Solution

**Concepts**

If the block slides, then kinetic frictional force is given by

**Explanations**:

**Given Data**:

In the problem (a) to (b): the box is stationary and the angle

Note: It is clear from Fig. 6-12, the angle

**Formula used:**

The free-body depiction for the inclined slope is provided below.

From Fig. (6-19) of the textbook and the free body diagram, we can draw:

No acceleration in the first case (from (a) to (d)) as the box is in the stationary position. Hence, acceleration is zero.

Applying Newton’s 2^{nd} law on the y-axis:

If the block slides, the kinetic frictional force:

If it does not slide, then the magnitude of maximum static friction:

**Calculations: **To find the magnitude of the different forces and their nature (increasing, decreasing, or no-change) when the angle (

(a) The horizontal component of the force is

(b) If a body does not move, the static frictional force and the component parallel to the surface are equal in magnitude, and is directed opposite that component. If the component decreases,

(c) The normal component of the force is given in Eq. (1).

The normal component of the force is

(d) From Eq. (3), the magnitude of the maximum static friction will also increase as

(e) In the sliding scenario, kinetic friction force can be explained by Eq. (2). This results in an increase in the kinetic frictional force. Thus, the friction force increases when the box slides and the angle between the surface and box increases.

**Conclusion**

If the value of the normal force

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# Chapter 6 Solutions

Fundamentals of Physics Extended

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