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Q14 CQ

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Found in: Page 315

### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# Explain why the forces in our joints are several times larger than the forces we exert on the outside world with our limbs. Can these forces be even greater than muscle forces?

The joints in human bodies act as a third-class lever. The mechanical advantage is less than 1.

See the step by step solution

## Step 1: Human hand as lever

The action of muscles when an object is placed on human hand palm is depicted as below:

Human hand as lever

The arm is represented by EP, Elbow at E, palm at P. The load of weight L is at palm.

The muscles exert a force ${F}_{M}$ upward, at a distance ${l}_{1}$from E. The center of mass of the forearm and the load are at distances ${l}_{2}$and ${l}_{3}$ from E.

## Step 2: Calculation of force

Under the equilibrium of forces, we can write,

${F}_{M}={F}_{E}+W+L..\dots \left(1\right)$

Here, W is the weight of the fore-arm.

Under the equilibrium of the moments about the point E,

$\begin{array}{l}{F}_{M}{l}_{1}=W{l}_{2}+L{l}_{3}\\ {F}_{M}=W\left(\frac{{I}_{2}}{{l}_{1}}\right)+L\left(\frac{{l}_{3}}{{l}_{1}}\right)........\left(2\right)\end{array}$

We can write from equation (1) that,

${F}_{E}={F}_{M}-\left(W+L\right)\phantom{\rule{0ex}{0ex}}=W\left(\frac{{l}_{2}}{{l}_{1}}\right)+L\left(\frac{{l}_{3}}{{l}_{1}}\right)-\left(W+L\right)\phantom{\rule{0ex}{0ex}}=W\left(\frac{{l}_{2}}{{l}_{1}}-1\right)+L\left(\frac{{l}_{3}}{{l}_{1}}-1\right)\phantom{\rule{0ex}{0ex}}$

As the factors,$\left(\frac{{I}_{2}}{{l}_{1}}-1\right)$ and$\left(\frac{{I}_{3}}{{l}_{1}}-1\right)$ are greater than unity,

${F}_{E}>W+L$