What is the Kinetic Friction?

Question

A penguin slides down an icy slope at a constant velocity. If the angle of the slope is 6.8 degrees what is the coefficient of kinetic friction between the penguin and the ice?

Answer 1

Friction force F_f is related to coefficient of kinetic friction μ and the normal force F_N by the equation

F_f=μF_N

where F_N=F_gcosθ=mgcosθ (F_g=force due to gravity=mg and θ=6.8 degrees in this case)

and the force due to gravity in the direction of travel is

F_downhill=F_gsinθ

Now let's balance the friction force, and it's opposite counterpart the downhill force - as they are equal at constant velocity.

F_downhill=F_f

mgsinθ=μmgcosθ

the "mg" terms cancel out, leaving

sinθ=μcosθ

μ=sinθ/cosθ (sin/cos=tangent)

μ=tanθ=tan(6.8°)=0.119