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”? (a) 4d (b) 2d (c) $\sqrt{2}d$ (d) d (e) d/2

To determine

The distance covered by truck after applying brakes.

Answer to Problem 1OQ

Option (d) the truck will cover the distance $d$.

Explanation of Solution

The distance covered by the truck after applying the brakes is given by the newton’s third equation of motion.

Write the expression for the distance covered by the truck as.

  $v^2=u^2-2aS$                                                                                                 (I)

Here, $v$ is the final velocity of the truck, $u$ is the initial velocity of the truck, $a$ is the retardation and $S$ is the distance covered through skidding.

From equation (I), the distance skid by the truck is independent of the mass of the truck.

Conclusion:

Substitute $d$ for $S$ in equation (I).

  $v^2=u^2-2ad$

To bring the truck carrying the double mass to rest, the truck will skid through the same distance as that of the truck with less mass.

For the truck, after applying the brakes, it will cover the same distance $d$ with a double mass on it. Thus, option (d) is correct.

The distance covered by the truck is independent of mass. So it will not cover $4d$. Thus, option (a) is incorrect.

The distance covered by the truck will not change when mass is increased so it will not cover $2d$. Thus, option (b) is incorrect.

The distance covered by the truck is independent of mass. So it will not cover distance $\sqrt{2}d$. Thus, option (c) is incorrect.

The distance covered is mass independent.so it will not cover $\frac{d}{2}$  Thus, option (e) is incorrect.