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.

 

[kyle8921]

I would like to point out that the equations and calculations provided in the attempt at a solution are correct. However, it is important to clarify that the CM height and the distance between the front and back tires are not interchangeable. The CM height, denoted as H in the sum torque equation, is the vertical distance from the center of mass to the ground, while the distance between the front and back tires, denoted as D, is the horizontal distance between the two points of contact with the ground.

In order to accurately calculate the normal forces on the inclined car, both the CM height and the distance between the front and back tires need to be taken into account. The sum torque equation is correct, but it can be rewritten as:

(Ff1 + Ff2)H + (N1-N2)(D/2)cos(theta) = 0

Where theta is the angle of inclination. This equation takes into account the torque caused by the car's weight and the normal forces on the front and back tires.

In conclusion, the attempt at a solution is correct, but it is important to clarify the difference between CM height and the distance between the front and back tires. Additionally, the sum torque equation should include the angle of inclination in order to accurately calculate the normal forces on the inclined car.