Chapter 5, Problem 7RQ

Why is it less damaging if you fall on a mat than if you fall on a solid floor?

To determine

The reason behind why it is less damaging when a person fall on a mat as compared to the person fall on a solid floor.

Answer to Problem 7RQ

The reason behind it is less damaging when a person fall on a mat as compared to a person fall on a solid floor because mat will exert small amount of force for long time interval.

Explanation of Solution

The quantity impulse is equal to the product of force exerted on the body and the time interval 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,

$p_2-p_1=Ft$

As the final momentum of the body becomes zero when the person falls on the floor. The expression can be written as,

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

The negative value of force indicates that a retarding force is acting on the body. From the above expression, it can be seen that the quantity force is inversely proportional over the time in which a person is brought to rest. Thus, a small-time will result in large force. When a person falls on a solid floor, he/she is brought to rest very quickly and so the time is very small. Hence, a large force is experienced by the falling person.

On the other hand, when the person falls on the mat, the time taken to come to rest is longer. Hence, a smaller force is experienced by the person. Hence, a smaller force will cause less injuries to the person.

Conclusion:

Therefore, the reason behind it is less damaging when a person fall on a mat as compared to the person fall on a solid floor because mat will exert small amount of force for long time interval.