Need Help Creating a Free Body Diagram of a Car on a Slope

mjgarrin

Hello. I have attached an image of a free body diagram of a car traveling up a ramp at 30 degrees. I was wondering if anyone can help me determine the sumation of forces in the X and Y direction.

I understand that the forces in the Y-direction must be equal to zero or else the car will not stay on the ground. This is the formula I have come up with for this problem:

u = coeff. of friction

FN = mg / cos30

Fu = u x FN

F = force the car is moving under its own power

Sum of Forces in Y direction: FN x cos30 - mg = 0

Is this the correct equation for finding the forces in the Y direction?

Sum of Forces in X direction: F - Fu - (mg x sin30) = ma

Is this the correct equation for finding the forces in the X direction?

Any help would be appreciated. Thank you!

Attached Thumbnails

 

tiny-tim

hello mjgarrin! welcome to pf!

(have a mu: µ and a theta: θ and a degree: ° )

first, your free body diagram is wrong, the mgcosθ is not a separate force and should not be there
no, the FN x cos30° and the mg are not in the Y direction, are they?
yes

jack action

See HPWizard.com for more info (At the bottom of the page --> Theory»»Longitudinal acceleration»»Accelerating»»Hill climbing)