Question

this is a 3 part question33) The human head can be considered as a 3.3-kg cranium protecting a 1.5-kg brain, with a small amount of cerebrospinal fluid that allows the brain to move a little bit inside the cranium. Suppose a cranium at rest is subjected to a force of 2800 N for 6.5 ms in the forward direction. (a) What is the finalspeed of the cranium? (b) The back of the cranium then collides with the back of the brain, which is still at rest, and the two move together. What is their final speed? (c) The cranium now hits an external object and suddenly comes to rest, but the brain continues to move forward. If the front of the brain interacts with the front of the cranium over a period of 15 m/s before coming to rest, what average force is exerted on the brain by the cranium?

Answer 1

Given data:

* The force applied is 2800 N.

* The time for which the force applied is 6.5 ms.

* The mass of the cranium is 3.3 kg.

Solution:

(a). The momentum of the cranium in the terms of the force applied is,

$p=Ft$

where F is the force applied, and t is the time,

Substituting the known values,

$\begin{gathered} p=2800\times6.5\times10^{-3} \\ p=18200\times10^{-3} \\ p=18.2kgms^{-1} \end{gathered}$

The velocity of the cranium from the momentum is,

$\begin{gathered} mv=p \\ v=\frac{p}{m} \end{gathered}$

where m is the mass of cranium including the brain inside it,

Substituting the known values,

$\begin{gathered} v=\frac{18.2}{3.3+1.5} \\ v=3.79\text{ m/s} \end{gathered}$

Thus, the final speed of the cranium is 3.79 m/s.