Friction on incline plane: Having trouble connecting math and intuition

[September24]

So the formula for friction on incline plane is:

F=(mu*k)*mg*cos


According to this, as angle of inclination increases, frictional force decreases. However, for some reason, shouldn't friction be doing more work on an object as angle increases (since there is more "component of gravity" down the ramp).

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[monkeyvokes]

the amount of friction force is due to mu*normal force, as you lift up the ramp you decrease the normal force

 

[September24]

Right...But as you increase the incline of a ramp, the object tends to slide down the ramp easier. Theres more of a force pushing it down the ramp so the static friction should be increasing to oppose that motion.

 

[t0ny]

The value for the normal force is actually mgcos(theta) so as you increase the angle of inclination, cos (theta) tends towards zero (it's minimum).

Watch out not to confuse these two:

Gravity down an incline =mgsin(theta)
Normal force down incline = mgcos(theta)

 

[monkeyvokes]

Right...But as you increase the incline of a ramp, the object tends to slide down the ramp easier. Theres more of a force pushing it down the ramp so the static friction should be increasing to oppose that motion.

true, and it will, to an extent. Then the object will begin to slide as gravity overcomes the remaining amount of friction (that is due to mu*Fnormal)

 

[TXKnight]

So the formula for friction on incline plane is:

F=(mu*k)*mg*cos


According to this, as angle of inclination increases, frictional force decreases. However, for some reason, shouldn't friction be doing more work on an object as angle increases (since there is more "component of gravity" down the ramp).

Normal force (force perpendicular to plane) in part determines your Ffriction, as you increase the angle, N gets smaller. Your contact force with the plane is actually smaller when you increase theta, thus friction is less. Think vectors.