I'm answering the following question, but am getting a different answer to the one given in the answers pages:
A body of mass 100g rests on a rough horizontal surface and has a light string, inclined at 20° above the horizontal, attached to it. When the tension in the string is 5 x $10^{-1}$ N, the body is found to be in limiting equilibrium. Find the coefficient of friction between the body and the surface.
I drew a diagram and resolved vertically to get R = 0.1g - 0.2sin(20)
Since it's in limiting equilibrium, the friction force F = $F_{max}$ = $\mu$R = $\mu$(0.1g - 0.2sin(20))
Then resolving horizontally gives F = 0.2cos(20), i.e. $\mu$(0.1g - 0.2sin(20)) = 0.2cos20, so $\mu$ = $\frac{0.2cos20}{0.1g - 0.2sin(20)}$ = 0.206
However, the answers in the back say that $\mu$ = 0.58
Where am I going wrong?! I can't work it out.
Many TIA!
A small typo caused the error. You should put the string tension to be $0.5$ instead of $0.2$, and you'll get the correct answer.