Calculating Normal Forces on Inclined Car - Torque Homework Solution

[inner08]

Homework Statement

A car of mass 1200kg has a distance (front to back) of 3.0m. On a horizontal surface, the front tires hold 60% of the weight. The CM is located at 0.8m off the road. Find the normal force on each wheel when the car is at rest on an incline of 20 degrees. The car is oriented in the sens of the hill.

Homework Equations

The Attempt at a Solution

I'm having some trouble putting all my forces together. I drew out an FBD but I'm not sure how to incorporate the CM and the front/back distance into the equations.

So far, this is what I have:

I figured one normal force for the front tires, and another normal force for the back tires.

Fy: N1 + N2 - Fg = 0
N1 + N2 - mgcos= 0

Fx: Ff1 + Ff2 = ma
-mgsintheta - mgsintheta = ma

sum torque: (Ff1 + Ff2)H + (N1-N2)D/2 = 0

H = CM height
D = distance between the front and back

I'm pretty sure the sum torque is wrong...but hopefully I atleast got the Fx and Fy correctly. Any help is appreciated!

Thanks,

 

[OlderDan]

I think you are missing something important about the CM. Try making a stick figure of the car on level ground with a horizontal line through the CM and two vertical lines to represent the wheels. (You have to assume the wheels are at the end of the car, since no other distance was given.) Where on the horizontal line is the CM? It is not in the middle.

After you locate the CM, rotate your figure to the incline of the hill and then calculate the torques about one point of contact between wheel and road.