Measuring the force exerted by muscles

In a nutshell

The muscles in the body enable movement by exerting forces on the bones when they contract. Using a formula, you can measure how much force a muscle applies to a bone. The study of how the skeleton moves when muscles exert force on the bones is called biomechanics.

Calculating the force

The moment of the weight

The force from a muscle causes the bone to rotate in its joint. The point where this rotation happens is also known as a pivot. This rotation/turning effect is called the moment of the force. Moments act about a pivot in either a clockwise or anticlockwise direction. To calculate the size of a moment, the following equation can be used:

$moment \space = \space force \space \times \space perpendicular \space distance$

In this equation:

$moment$	$newton \space metres \space (Nm)$
$the \space force \space of \space the \space weight$	$newtons \space (N)$
$perpendicular \space distance$	$metres \space (m)$

The force applied by the muscle

Once the moment has been calculated, the equation can be rearranged to calculate the force applied by a specific muscle. This is because there are two forces in action. The force of the weight is counteracted by the force of the muscle in action in order to keep the body still. Therefore, the moment of the muscle is equal to the moment of the weight.

$force \space = \space {moment \over perpendicular \space distance}$

Example

A boy lifts an apple with his hand. Calculate the force applied by the muscle in the arm.

Science; Human skeleton and muscles; KS3 Year 7; Measuring the force exerted by muscles — 1. Apple ( $10 \space N$ ), 2. Muscle, 3. Tendon, 4. Elbow (pivot), 5. Distance between the pivot and the muscle ( $0.04 \space m$ ), 6. Distance between the pivot and the apple ( $0.25\space m$ )

First, calculate the moment of the weight:

$10 \space N \space (force) \space \times \space 0.25 \space m \space (perpendicular \space distance) \space = \space 2.5 \space Nm \space (moment)$

Then, rearrange to calculate the force applied by the muscle:

${2.5 \space Nm \space (moment)\over 0.04 \space m \space (perpendicular \space distance)}= \underline6\underline2\underline.\underline5\underline \space\underline N$

$\underline{Therefore,\ the\ force\ applied\ by\ the\ muscle\ is\ 62.5\ N.}$