How Do You Calculate the Coefficient of Friction on an Inclined Plane?

[patton_223]

Homework Statement

A 5kg block slides down an inclined plane at constant velocity. If the angle of inclination is 22 degrees, find the coefficient of friction.

Homework Equations

F=ma
trig

The Attempt at a Solution

I'm only able to find the normal force, i suppose i could also use 98sin22 to get 36.71 but is this my net force? i just was never asked a question like this in particular before

 

[Elwin.Martin]

The key to figuring out the net force is the phrase:
"constant velocity"

In order to have a constant velocity, there must be 0 change in momentum
Forces are just change in momentum per change in time (when you take calculus it's the derivative of momentum).
So if the change in momentum is 0 then the sum of the forces, or net force, is equal to 0.

I'm hoping you can figure out the rest from here, if not let me know.

 

[LogicFreak]

First you need to find the component of the block's weight in the direction of the motion. Multiply 5kg by 9.81 m/s^2 to find the weight. Now multiply this by the cosine of 22 degrees ( 5 x 9.81 x cos22). This will give you the force acting against friction.

Note: it always helps to draw a triangle on the side when solving for trig equations.

Because the block is moving constant velocity, this force you just found is being counteracted (or balanced) by the force of friction. Meaning they are equal. Now that you know the force of friction, you can solve for the coefficient of friction.

Normal force x coefficient of friction = force of friction. Plug in your numbers and divide.