Troubleshooting Trigonometry: Finding Coefficient of Friction on a Slope

[Glype11]

This problem deals with finding the coefficient of friction between an object and a slope. It gives an object with mass m, sliding down a hill with a slope of θ at a constant velocity. I got mgsinθ=fksinθ.
However the book shows mgsinθ=fk. The kinetic friction force and the force down the slope are parallel but directed in opposite directions, so where is my error? I included a drawing for reference.

 

[Nathanael]

I'm assuming "fk" is "F_k" which is the force of kinetic friction?

The direction of kinetic friction is naturally in the opposite direction as the motion, so what was your reasoning for multiplying it by sin(θ)?

I got mgsinθ=fksinθ.

That can just be simplified to mg=F_k

Does mg=F_k make sense to you? That would imply that the angle θ is irrelevant. Does that seem right?

 

[Nathanael]

so where is my error?

No one can really tell you your error unless you take us through the train of thought that led you to your answer (which you didn't explain).How does the fact that it's moving at a constant velocity effect this problem?

 

[Glype11]

No one can really tell you your error unless you take us through the train of thought that led you to your answer (which you didn't explain).


How does the fact that it's moving at a constant velocity effect this problem?

Because it is constant velocity the down slope component of gravity must balance the frictional force. I figured out my error.