Question

A worker can supply a maximum pull 150 lb on a cart which has a handle set at an angle
of 40o
above the horizontal. What is the coeficient of friction if he can just move a total
load 1,500lb?

Answer 1

Assume the worker moves the cart so it moves at a constant speed. Forces acting along the horizontal:

$$F\text{ cos}40°-f=0.\\ f=\mu N,\\\space\\ \mu N=F\text{ cos}40°=0,\\\space\\ \mu=\frac{F\text{ cos}40°}{N}.$$

Forces along the vertical:

$$N-mg-F\text{ sin}40°=0.\\\space\\ \mu=\frac{F\text{ cos}40°}{N}=\frac{F\text{ cos}40°}{mg+F\text{ sin}40°}=0.07.$$