Calculating Muscle Force

This lesson covers: 

1. How bones act as levers moved by muscle forces
2. The calculations used to determine muscle force

Quantifying muscle force

Our skeleton contains many bones that function as levers.

These levers pivot and move when forces are applied by muscles.

We can use physics equations to calculate the force exerted by a muscle.

Calculating moments in an arm lever

Let's examine how to determine the force created by a muscle in the arm:

1. A pivot point enables rotation of a lever. The elbow is the pivot for the arm lever.
2. When a force acts on a lever, it generates a 'rotational effect' called a moment.
3. With the elbow as the pivot, the arm operates as a lever. Forces on the arm produce moments.
4. We can calculate moments using this formula:

Moment = force × perpendicular distance

Worked example - Calculating moments

A weight generates a moment on the arm lever. The weight force is 12 N and it's 0.3 m from the elbow.

Calculate the moment generated by the weight on the arm lever.

Step 1: Equation

Moment = force × perpendicular distance

Step 2: Substitution

Moment = 12 × 0.3

Step 3: Correct evaluation

Moment = 3.6 N m

Determining muscle force

In the example above, the weight isn't the only force - the muscle also applies a force.

This muscle force counterbalances the weight's moment to keep the arm stationary.

For equilibrium, the muscle's moment must equal the weight's moment (with opposite direction).

Worked example - Determining muscle force

A weight's moment is 3.6 N m and the muscle's distance to the elbow pivot is 0.05 m.

Rearrange the moment formula to find the muscle force.

Step 1: Equation

Moment = force × perpendicular distance

Step 2: Rearrangement

Force = perpendicular distancemoment​

Step 3: Substitution

Force = 0.053.6​

Step 4: Correct evaluation

Muscle force = 72 N