Chapter 5, Problem 1TE

When rollerblading, why is a fall less harmful on a wooden floor than on a concrete floor that has less give? Explain in terms of impulse and momentum.

To determine

The reason behind the fact that it is less harmful to fall on a wooden floor than on a concrete floor.

Answer to Problem 1TE

The reason behind the fact that it is less harmful to fall on a wooden floor that on a concrete floor is that wooden floor increases the time of impact resulting in less injury.

Explanation of Solution

A person gains momentum while doing the rollerblading because of its mass and velocity.

Write the expression for the impulse.

$I=Ft$

Here,

$F$ is the force

$t$ is the time

Write the alternative expression for the impulse.

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

Here,

$p_1$ is the initial momentum

$p_2$ is the final momentum

Equate the above two equations for change in momentum.

$p_2-p_1=Ft$

As the final momentum of the body becomes zero when the person falls on the floor, the final velocity is zero which means the final momentum will also be zero.

Substitute $0$ for $p_2$ in the above expression to get $F$.

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

From the above expression, it can be seen that the impact force experienced by the person is inversely proportional to the time interval. When a person falls while doing rollerblading, momentum changes to zero. So when he/she falls on a concrete floor, the time of impact will be much shorter, due to which a greater amount of force is exerted by the floor on the person. Since the impact force is higher, the person will face more injury. Whereas, when he/she falls on a wooden floor, the impact time is longer as the wooden floor is softer than concrete. This will result in a smaller amount of impact force on the person, which will cause less injury.

Conclusion:

Therefore, the reason behind the fact that it is less harmful to fall on a wooden floor that on a concrete floor is that wooden floor increases the time of impact resulting in less injury.