What Is the Minimum Force to Keep a Sled From Slipping on an Inclined Plane?

[Stianos]

1. A loaded penguin sled weighing 70 N rests on a plane inclined at 20° to the horizontal. Between the sled and the plane the coefficient of static friction is 0.25, and the coefficient of kinetic friction is 0.16.
(a) What is the minimum magnitude of the force F, parallel to the plane, that will prevent the sled from slipping down the plane?

3. I cannot figure out what I'm doing wrong. I draw my free body diagram, write out an x/y chart, and then solve.
I write a lot, so I'm just post an imgur link with my work in it.
http://imgur.com/pCNNQ

Can anyone show me what I'm doing wrong?

 

[TSny]

Hello, Stianos.

If the sled is on the verge of slipping down the slope, what is the direction of the friction force?

Also, looks like you're treating the coefficient of friction as being the same as the force of friction.

 

[Stianos]

If the sled is on the verge of slipping down the slope, then the friction is pointing up the slope?
Should I not do that? What should I do instead?
Thank you for responding, sorry I couldn't not respond immediately.

 

[TSny]

If the sled is on the verge of slipping down the slope, then the friction is pointing up the slope?

Yes. It looked to me that you had the friction pointing down the slope.

 

[Nickie]

I understand your frustration and desire to find the correct solution to this problem. From looking at your work, it seems that you have correctly identified the forces acting on the sled and have set up your equations correctly. However, it is possible that you may have made a mistake in your calculations or used incorrect values for the coefficients of friction. I would suggest double checking your calculations and making sure you are using the correct values for the coefficients. Additionally, it may be helpful to try solving the problem using different methods to see if you get the same result. If you continue to have trouble, I would recommend seeking assistance from a teacher or tutor who can provide you with additional guidance and support. Remember, the process of problem solving is just as important as getting the correct answer, so don't get discouraged and keep trying.