Static friction on inclined surface

[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?

 

[wavingerwin]

force down the slope:
F_d = mg sin 56⁰

normal force:
N = mg cos 56⁰

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

maximum force provided by string
F_s = 152

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

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

Hope this is correct and helps

 

[drkidd22]

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

Thanks for your help.

 

[wavingerwin]

well, i was just being a little bit fancy

if you want, i think you can use

F_d = $$\mu$$N + F_s

the previous equation:
F_d $$\leq$$ $$\mu$$N + F_s
just means that the force pulling the boy down must be less than or equal to the force holding the boy up (F_r and F_s)
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.