Torque Example
1.) Prof. Springer is doing his usual workout at the gym. Like always, he is doing bicep
curls with a 60 lb weight in each arm. The distance from his elbow joint (axis of
rotation) to his palm (where the weight is located) is 45 cm. Suppose his bicep is
currently 30◦ below the horizontal (total opening angle is 120◦ ). How much force (in
Newtons) must his bicep muscle exert in order to keep the weight steady? The bicep
tendon is inserted at a distance of 5.0 cm from the elbow joint. (See diagram). You
may ignore the torque due to the weight of the arm itself. Assume that the force from
the bicep muscle acts exactly vertically.
Solution: For the arm to hold steady, the torques must be equal and opposite. To
compute the torques we use the product of the force and the lever arm.
τbicep = Fbicep dbicep
τweight = Fweight dweight .
(1)
(2)
(3)
The lever arms are found from the diagram.
√
3
Fbicep rbicep
2
√
3
◦
= Fweight rweight sin(60 ) =
Fweight rweight
2
◦
τbicep = Fbicep rbicep sin(120 ) =
τweight
(4)
(5)
Thus, we should have
Fbicep = Fweight
rweight
rbicep
Fbicep rbicep = Fweight rweight
45 cm
= 60 lbs ×
= 540 lbs
5 cm
1
(6)
(7)
Now, convert to newtons:
540 lbs ×
4.448N
= 2402 N
1 lb
Muscles must exert a lot of force, since they act so close to the axis of rotation!
2
(8)