Chapter 9.2, Problem 50E

a.

To determine

Find the weight of the car.

Answer to Problem 50E

  $w\approx 2822Ib$

Explanation of Solution

Given information:

A car is inclined $10°$ to the horizontal. $490Ib$ of force is required to keep the car from rolling down the driveway.

Calculation:

Consider the assumption diagram regarding car’s situation,

  

It given that inclined $10°$ to the horizontal and force of $490Ib$ is required to keep the car from rolling down the driveway.

According to the diagram,

  $u$ ,represents the force that required to keep the car from rolling down the driveway. $w$ represents the weight of the car acting downward, $v$ , represents the force that will be experienced by the surface.

Now,

  $\begin{array}{l}\left|u\right|=\text{Component of w along u}\\ \text{490=w cos80}°\\ \text{w=}\frac{490}{\text{cos80}°}\\ w=2821.7\approx 2822\end{array}$

Hence, weight of the car is, $w\approx 2822Ib$

b.

To determine

Find the force car exerts against the driveway.

Answer to Problem 50E

  $v\approx 2799Ib$ .

Explanation of Solution

Given information:

A car is inclined $10°$ to the horizontal. $490Ib$ of force is required to keep the car from rolling down the driveway.

Calculation:

Consider the assumption diagram regarding car’s situation,

  

It given that inclined $10°$ to the horizontal and force of $490Ib$ is required to keep the car from rolling down the driveway.

According to the diagram,

  $v$ , represents the force that will be experienced by the surface.

Now,

  $\begin{array}{l}\left|v\right|=\text{Component of w along v}\\ \text{=w cos10}°\\ =2822\text{cos10}°\\ =2779.12\approx 2799\\ v\approx 2799Ib\end{array}$

Hence, the force the car exerts against the driveway is, $v\approx 2799Ib$ .