Chapter 5, Problem 6RQ

If you’re in a car with faulty brakes and you have to hit something to stop, the momentum will change to zero whether you hit a brick wall or a haystack. So why is hitting a haystack a safer bet?

To determine

The reason behind hitting a haystack is a safer bet as compared to a brick wall.

Answer to Problem 6RQ

The reason behind hitting a haystack is a safer bet as compared to a brick wall because haystack will exert small force resulting in less damage.

Explanation of Solution

The impulse is the quantity imparted to a body, which is equal to the multiplication of force applied on the object and the time for which the force is acting. This can be expressed as,

$I=Ft$

Here,

$F$ is the force

$t$ is the time

The quantity impulse of an object is equal to the change in momentum, which can be represented as,

$\begin{array}{l}I=\Delta p\\ I=p_2-p_1\end{array}$

$p_2$ is the final momentum

$p_1$ is the initial momentum

So, it can be written as,

$p_2-p_1=Ft$

When the object comes to rest, the final momentum becomes zero. Thus, the expression can be written as,

$\begin{array}{c}Ft=0-p_1\\ F=-\frac{p_1}{t}\end{array}$

The negative force value indicates that a retarding force is acting on the body. The quantity force is inversely proportional over the time in which a person is brought to rest, which can be seen from the above expression. Thus, a small-time will result in large force. In the case, when a car hits a brick wall, the car comes to rest in a very small amount of time. As a result, a larger force will be exerted on the car, causing more damage and injury to the car and occupant. On the other hand, when the car hits the haystack, the time taken by the car to come to rest becomes more. Hence, a smaller force is experienced by the car, resulting in less damage and injuries.

Conclusion:

Therefore, the reason behind hitting a haystack is a safer bet as compared to a brick wall because haystack will exert small force resulting in less damage.