Question

A car runs out of gas while driving down a hill. It rolls through the valley and starts up the other side. At the very bottom of the valley, which of the free-body diagrams in FIGURE Q8.2 is correct? The car is moving to the right, and drag and rolling friction are

negligible.

Short answer

Option a is the best suitable free body diagram for this car.

Step-by-step solution

Given information

A car runs out of gas while driving down a hill. It rolls through the valley and starts up the other side.

Proof:

We can analyze the situation quantitatively by writing the r-component of Newton’s second law. At the bottom of the circle, with the r-axis pointing upward, we have

$\sum _{}{F}_r=n_r+{\left(F_G\right)}_r=n-mg=m{a}_r=\frac{m{\left(v_{car}\right)}^2}{r}$

From the above equation, we find,

$n=mg+\frac{m{\left(v_{car}\right)}^2}{r}$

The normal force at the bottom is larger than mg. The normal force of the track pushes up when the car is at the bottom of the circle.

Explanation

The normal force at the bottom is larger than mg. The normal force of the track pushes up when the car is at the bottom of the circle. Option a in the given FIGURE Q8.2 is the suitable free body diagram.