Answer to Question #280093 in Physics for Faith

Question

A bodybuilder holds a dumbbell of weight Wd. His arm is horizontal and weighs 37 N. The deltoid muscle is assumed to be the only muscle acting and is attached to the arm as shown. The maximum force M→ that the deltoid muscle can supply has a magnitude of 1887 N. The distances that locate where the various forces act on the arm. What is the weight of the heaviest dumbbell that can be held by the bodybuilder?

Answer 1

Find the weight of the heaviest dumbbell that the bodybuilder can hold is

$$Fl-W_a\frac L2-W_dL=0,\\\space\\ W_d=\frac {Fl}L-\frac{W_a}2=\bigg(1887\frac lL-18.5\bigg)\text{ N}.$$

$l$ is the distance from the shoulder joint to the point where the muscle is attached,

$L$ is the length of the arm.