Static Equilibrium of an automobile

[Seraph404]

Homework Statement

An automobile with a mass of 1360 kg has 3.05 m between the front and rear axles. Its center of gravity is located 1.78 m behind the front axle. With the automobile on level ground, determine the magnitude of the force from the ground on a) each wheel (assuming equal forces on the front wheels) and b) each rear wheel (assuming equal forces on the rear wheels).

Homework Equations

Forces up = forces down
Forces to the right = forces to the left
Net torque clockwise = net torque counter-clockwise

In other words, net force = 0

The Attempt at a Solution

N = mgr
a) r being the distance from the front axel to the center of gravity
b) r being the distance from the center of gravity to the rear axel

Is this correct?
I sort of drew a picture, but I'm not able to scan it at the moment.

 

[PaintballerCA]

N=mgr is incorrect. Write out the units for that equation and see what you get. What units do you need?

I suggest you draw your free body diagram in Microsoft paint or something so that you can post it. This type of problem becomes extremely simple with the correct free body diagram.

 

[Moetasim]

I can confirm that your approach and equations are correct. To determine the force from the ground on each wheel, you need to consider the forces acting on the car in a static equilibrium. This means that the net force and net torque must be equal to zero, as you have correctly stated.

To find the magnitude of the force on each wheel, you can use the equation F = ma, where m is the mass of the car and a is the acceleration, which is zero since the car is in static equilibrium. The force on each wheel will be equal to half of the weight of the car, or half of the product of mass and gravity (mg/2).

For the front wheels, the distance from the front axle to the center of gravity is 1.78 m, so the force on each front wheel would be (1360 kg)(9.8 m/s^2)/2 = 6676 N. Similarly, for the rear wheels, the distance from the center of gravity to the rear axle is 1.27 m (3.05 m - 1.78 m), so the force on each rear wheel would be (1360 kg)(9.8 m/s^2)/2 = 6676 N.

Overall, your approach and calculations are correct. Good job!