Chapter 9.2, Problem 49E

(a)

To determine

To find: The weight of the car rolling down from the driveway.

Answer to Problem 49E

The weight of the car rolling down from the driveway is 2822.

Explanation of Solution

Given:

The angle formed by the car to the horizontal axis is $10°$.

The force required to keep the car rolling down the driveway is 490 lb.

Calculation:

The figure below shows that the car is on a driveway that inclined an angle of $10°$ with horizontal.

Figure (1)

From Figure (1), it can be observed that the car exerts force into two components u and v.

The angle formed between u and w is,

$\begin{array}{c}\theta =90°-10°\\ =80°\end{array}$

The magnitude of force that prevents the car from rolling down the driveway is,

$F=\left|u\right|=\text{component}\text{of}w\text{along}u=w\cos \theta$

Substitute 490 for F and $80°$ for $\theta$ in the above formula.

$\begin{array}{c}490=w\cos 80°\\ w=\frac{490}{0.173}\left(\cos 80°=0.173\right)\\ =2821.79\approx 2822\end{array}$

Thus, the weight of the car rolling down from the driveway is 2822.

(b)

To determine

To find: The force exerted by the car against the driveway.

Answer to Problem 49E

The force exerted by the car against driveway is 2779 lb.

Explanation of Solution

Given:

The angle formed by the car to the horizontal axis is $10°$.

The force required to keep the car rolling down the driveway is 490 lb.

Calculation:

The magnitude of the force exerted by the car on the driveway is,

$\begin{array}{c}F=\left|v\right|=\text{component}\text{of}w\text{along}v\\ =w\text{sin}\theta \end{array}$

Substitute 2822 for w and $80°$ for $\theta$ in the above formula.

$\begin{array}{c}F=2822\times \text{sin80}°\\ =\text{2822}\times \text{0}\text{.984}\left(\because \sin 80°=0.984\right)\\ =2779.127\approx 2779\end{array}$

Thus, the force exerted by the car against driveway is 2779 lb.