Calculating Frictional Force of a Sliding Mass

[zedx]

Homework Statement

A 10.0-kg mass is placed on a 25.0o degree incline and friction keeps it from sliding. The
coefficient of static friction in this case is 0.580, and the coefficient of sliding friction is
0.520. The mass is given a shove causing it to slide down the incline.

Homework Equations

What is the frictional
force while the mass is sliding?

The Attempt at a Solution

This is all I have so far, but I don't exactly understand it:

Frictional force while the mass is sliding = μmgcosθ = 0.52 X 10 X 9.8 X cos 25
= 46.19 N


I need a full step-by-step explanation, if possible. I'll also take any other information about the problem that may make it easier. Thank you.

 

[Delphi51]

Your 46.19 is correct.
You also need to find the downward, along the ramp force. It is the other component of mg, that is mg*sin(25). The net force along the ramp is this force minus the friction force.

I always draw the ramp, put the mass at the very top and draw the mg force vector straight down. Then separate that mg into the sum of a force along the ramp and perpendicular to the ramp. The perpendicular force is the normal force pulling the mass against the ramp surface.

 

[Simon Bridge]

Welcome to PF;
Draw a free-body diagram for the mass and you'll see how that relation was found.

 

[zedx]

Your 46.19 is correct.
You also need to find the downward, along the ramp force. It is the other component of mg, that is mg*sin(25). The net force along the ramp is this force minus the friction force.

I always draw the ramp, put the mass at the very top and draw the mg force vector straight down. Then separate that mg into the sum of a force along the ramp and perpendicular to the ramp. The perpendicular force is the normal force pulling the mass against the ramp surface.

Welcome to PF;
Draw a free-body diagram for the mass and you'll see how that relation was found.

I'll do all of the above. Thank you.

 

[Simon Bridge]

Cool! Let us know how you get on.