# Static friction on inclined surface

1. Oct 20, 2009

### drkidd22

Hello all.

I'm having issues trying to figure out the following problem.

A boy with a mass of 52 kg and on a 56-degree slope is hanging on to a cord with a breaking strength of 152 newtons. What must be the coefficient of static friction between the boy and the surface?

2. Oct 21, 2009

### wavingerwin

force down the slope:
Fd = mg sin 560

normal force:
N = mg cos 560

Friction holding the boy
Fr = $$\mu$$N

maximum force provided by string
Fs = 152

Equating forces:
the string must not break so the boy doesn't fall, so
Fd $$\leq$$ $$\mu$$N + Fs

you can the solve for $$\mu$$, the coefficient of friction

Hope this is correct and helps

3. Oct 21, 2009

### drkidd22

This works well. I had gotten almost everything together. The only thing I couldn't figure out was the equation of the forces.

4. Oct 22, 2009

### wavingerwin

well, i was just being a little bit fancy

if you want, i think you can use

Fd = $$\mu$$N + Fs

the previous equation:
Fd $$\leq$$ $$\mu$$N + Fs
just means that the force pulling the boy down must be less than or equal to the force holding the boy up (Fr and Fs)
The only unknown variable is $$\mu$$, so as long as $$\mu$$ is big enough so that friction force is big, the boy would not fall.