Question

You pull a big block (60 kg) at constant velocity along the dirt by pulling with a force of 200 N on a rope at an angle of 30 degrees. What is the coefficient of kinetic friction between the box and the ramp?
I know the answer is .35 but I'm not sure how to do it.

Answer 1

Start with your free body diagram. First thing to notice is that your force is not parallel to the work, instead it is at an angle. So you need to break the force up into its components. Recall from your trig functions that to find the sides of a triangle you use SOH CAH TOA, so to find the x component of your force you need to use an angle and hypotenuse to calculate the adjacent:\[\cos(\theta)=\frac{adj}{hyp} \rightarrow \cos(\theta)\times hyp=adj \rightarrow \cos(30) \times 200N=173.2N\]Now just like before you are moving at a constant velocity so your forces will balance. So your horizontal forces are 173.2N being countered by the force of friction. Friction you know is just mu times the weight (mg), so setting it up just like before you can solve for your frictional coefficient. \[F_x - F_{fric}=0 \rightarrow F_x- \mu mg=0 \rightarrow \mu =-(\frac{-F_x}{mg})\] Although I am not sure where you got 0.35 from.