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Q17 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

# If the maximum force the biceps muscle can exert is ${\mathbf{1000}}{\mathbf{}}{\mathbf{N}}$, can we pick up an object that weighs${\mathbf{1000}}{\mathbf{}}{\mathbf{N}}$? Explain your answer.

The maximum force the biceps muscle can exert is$1000\mathrm{N}$ , we can pick objects less than that weighs$1000\mathrm{N}$ .

See the step by step solution

## Step 1: Force

A force is an external factor that can change the rest or motion of a body. It has a size and a general direction.

## Step 2: Human hand as lever

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

Human hand

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 3: Calculation of force

Under the equilibrium of forces, we can write,

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

Under the equilibrium of the moments about the point E,

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

We can write from equation (2) that $\left(\frac{{I}_{2}}{{I}_{1}}\right)$ and $\left(\frac{{I}_{3}}{{I}_{1}}\right)$ are greater than 1. So, the force,

${F}_{M}>L$

Hence, the maximum force the muscle can exert is $1000\mathrm{N}$ , it can lift only less than $1000\mathrm{N}$.