Chapter 5, Problem 1OQ

The driver of a speeding empty truck slams on the brakes and skids to a stop through a distance d. On a second trial, the truck carries a load that doubles its mass. What will now be the truck’s “skidding distance”?

1. (a) 4d
2. (b) 2d
3. (c) $\sqrt{2}d$
4. (d) d
5. (e) d/2

To determine

Skidding distance of truck from the given options.

Answer to Problem 1OQ

Option (d).

Explanation of Solution

Write the expression for skidding distance of the car.

    $d_i=\frac{v^2}{2\mu g}$

Here, $v$ is the initial speed, $d_i$ is the initial skidding distance, $\mu$ is the coefficient of friction, and $g$ is the acceleration due to gravity.

The stopping distance does not depend on the mass. Even the mass of the truck increases two times, the stopping distance remains same. If the normal force and frictional force both doubled, so the backward acceleration remains same as without the load.

Conclusion:

Since stopping distance does not depend on mass, option (d) is correct.

Stopping distance does not depend on mass. Thus, option (a) is incorrect.

Stopping distance does not depend on mass. Thus, option (b) is incorrect.

Stopping distance does not depend on mass. Thus, option (c) is incorrect.

Stopping distance does not depend on mass. Thus, option (e) is incorrect.