Chapter 6, Problem 77RE

Solution

(a)

To find: The force required to keep the car from rolling down the hill.

The force required to keep the car from rolling down the hill is $826.91\text{ lb}$ .

Given information:

Weight of car $=3000\text{ lb}$

Angle made by street with the horizontal $=16°$

Formula used:

The force of gravity, $F$ , is acting on a body kept on street. The components of $F$ are $F\cos \theta$ and $F\sin \theta$ .

  $F\cos \theta$ acts perpendicular to the street and $F\sin \theta$ acts along the street.

Calculation:

Let $F$ be the force of gravity acting on the car.

Component of force acting along street is $F\sin \theta$ .

  $\begin{array}{c}F\sin \theta =3000\times \sin 16°\\ =826.91\end{array}$

Therefore, the force required to keep the car from rolling down the hill is $826.91\text{ lb}$ .

(b)

To find: The component of the force perpendicular to the street.

The component of the force perpendicular to the street is $2883.7\text{ lb}$ .

Given information:

Weight of car $=3000\text{ lb}$

Angle made by street with the horizontal $=16°$

Formula used:

The force of gravity, $F$ , is acting on a body kept on street. The components of $F$ are $F\cos \theta$ and $F\sin \theta$ .

  $F\cos \theta$ acts perpendicular to the street and $F\sin \theta$ acts along the street.

Calculation:

Let $F$ be the force of gravity acting on the car.

Component of force acting perpendicular to the street is $F\cos \theta$ .

  $\begin{array}{c}F\cos \theta =3000\times \cos 16°\\ =2883.7\text{ lb}\end{array}$

Therefore, the component of the force perpendicular to the street is $2883.7\text{ lb}$ .