# The mass of an automobile is 1160kg, and the distance between its front and rear axles is 2.54m. The center of gravity of the car is between the front and rear tires, and the horizontal distance between the center of gravity and the front axle is 1.02m. Determine the normal force that the ground applies to (a) each of the two front wheels and to (b) each of the two rear wheels.

PLEASE GIVE ME SOME HINTS TO DO IT...THANKS A LOT!

## The total force on the four tires is the weight of the car:

m g = 1160 * 9.8

Now do a see saw

You have m g down at 1.02 meters behind the front axle

You have 2Fb up at the rear tires,2.54 meters behind the front axle (I called it two Fb so I will not forget to divide by two to get each of the rear tires.)

take moments (torques) about the front axle

2Fb * 2.54 = m g * 1.02

solve that for Fb, the force on the back axle

then the total force up = total force down

so

2Fb + 2Ff = m g

You know mg and your know 2Fb so now you know 2Ff

divide 2Ff by two to get the force on each front wheel

divide Fb by two to get the force on each rear wheel

## The total force on the four tires is the weight of the car:

m g = 1160 * 9.8

Now do a see saw

You have m g down at 1.02 meters behind the front axle

You have 2Fb up at the rear tires,2.54 meters behind the front axle (I called it two Fb so I will not forget to divide by two to get each of the rear tires.)

take moments (torques) about the front axle

2Fb * 2.54 = m g * 1.02

solve that for 2Fb, the force on the back axle

then the total force up = total force down

so

2Fb + 2Ff = m g

You know mg and your know 2Fb so now you know 2Ff

divide 2Ff by two to get the force on each front wheel

divide 2Fb by two to get the force on each rear wheel

## Ok, so after struggling through the above explanation I decided to repost a (imho) better worded, generalized explanation:

Firstly let me define my variables: Fb=force of BOTH back wheels on the ground=2F(1backwheel)

Ff=force of BOTH front wheels on the ground=2F(1frontwheel)

d1= distance of back wheels from front

d2= distance of CM from front wheels

We should first recognize that the force of the ground on both back wheels is equal in magnitude (but opposite indirection) to the force of the wheels on the ground or Fb=F(ground.on.back.wheels)and the force of the ground on the front wheels is equal to the force of the front wheels on the ground or Ff=F(ground.on.front.wheels).

We know that the force of the ground on all four wheels is equal to the force of weight of the car (mg)because the car isn't falling through the ground.

So F(ground.on.back.wheels)+F(ground.on.front.wheels)= mg = Fb+Ff

Define down as positive:

Now if we act as though the car could rotate around the front axle and recognize that the net torque is 0 then we know that Torque at CM + torque at back caused by ground=0=d2*mg+ d1*(-F(ground.on.back.wheels) so F(g.o.b.w)=mg(d2/d1)= magnitude of Fb

which is twice the magnitude of the force of each back wheel.

Use Fb+Ff=mg to find Ff which is twice the magnitude of the force of each front wheel

## To determine the normal force on the wheels, we need to consider the weight distribution of the car. The normal force is the force exerted by a surface perpendicular to the object on that surface.

Hint for part (a):

To determine the normal force on each of the two front wheels, we need to calculate the weight distribution of the car between the front and rear axles. Since the center of gravity is between the front and rear tires, we can assume the weight is evenly distributed between the two axles. You can use the equation:

Weight Distribution = (Distance from the center of gravity to the rear axle) / (Distance between the front and rear axles)

Hint for part (b):

To determine the normal force on each of the two rear wheels, we can again assume the weight is evenly distributed between the front and rear axles. The weight distribution can be calculated using the same equation:

Weight Distribution = (Distance from the center of gravity to the front axle) / (Distance between the front and rear axles)

Once you have the weight distribution, you can calculate the normal force on each wheel by multiplying the weight distribution by the total weight of the car (which is the mass of the car multiplied by the acceleration due to gravity, g = 9.8 m/s^2).

Normal Force = Weight Distribution * Total Weight

Remember to convert the mass of the car from kg to Newtons by multiplying it by the acceleration due to gravity.