Question

True or False: The forces applied by our muscles on our bones are usually several times larger than the forces we exert on the outside world with our limbs.

Answer 1

True

Step-by-step explanation:

This is because of the point where the forces are applied by our muscles and

the angle they have about the bones. Take for example the diagram I uploaded.

If we do a free body diagram and a sum of torques, we would get that:

`F_(muscle)sin \theta r1 - mg r2 = 0`

In this case, mg is the same in magnitude as the force made by the hand to hold the ball, so:

`F_(muscle)sin \theta r_(1) - F_(hand) r_(2) = 0`

If we solve the equation for the force of the muscle we would get that:

`F_(muscle)=(F_(hand)r_(2))/(r_(1)sin \theta)`

Since r2 is greater than r1 and the sin function can only return values that are less than 1, this means that the force of the muscle is much greater than the force used by the hand to hold the weight.

Let's use some standard values to prove this, let's say that r1=10cm, r2=35cm and theta=60 degrees. When inputing the values into the equation we get:

`F_(muscle)=(F_(hand)(35cm))/((10cm)sin (60^(o)))`

which yields:

`F_(muscle)=4.04 F_(hand)`

so in this example, the force made by the muscle is 4 times as big as the force exerted by the hand.