Question

Braking Load A Pontiac Bonneville with a gross weight of $4500$pounds is parked on a street with a ${10}^{\circ }$grade. Find the magnitude of the force required to keep the Bonneville from rolling down the hill. What is the magnitude of the force perpendicular to the hill?

Short answer

The magnitude of the force required to keep the Bonneville from rolling down the hill is $783$pounds and the magnitude of the force perpendicular to the hill is$4432.5$pounds.

Step-by-step solution

Step 1. Given Information 

The gross weight of a Pontiac Bonneville is $4500$pounds and it is parked on a street with a ${10}^{\circ }$grade. We have to find the magnitude of the force required to keep the Bonneville from rolling down the hill and the magnitude of the force perpendicular to the hill.

Step 2. Finding the force

Let the force be into components going down the hill.

So, the force required to keep the Bonneville from rolling down the hill is

$$\begin{gathered} F=4500\left(\sin 10°\right) \\ F=4500\left(0.174\right) \\ F=783\mathrm{pounds} \end{gathered}$$

Step 3. Finding the force

Let the force be into components perpendicular to the hill.

So, the magnitude of the force perpendicular to the hill is

$$\begin{gathered} F=4500\left(\cos 10°\right) \\ F=4500\left(0.985\right) \\ F=4432.5\mathrm{pounds} \end{gathered}$$