A car negotiates a curve of 120m radius on a horizontal road at a speed of 80 km/h. The mass of the car?

Question

is 1200 kg, its centre of mass is 650mm above the road surface and its wheel spacing (across the car) is 1.6m. Calculate the total vertical force exerted by the wheels on each side of the car, assuming an equal distribution between front and rear axles.

Could you show your working as a i cant calculate the correct answer

Answer 1

The centripetal force because the car is negotiating a curve is
m*v^2/r
or
1200*(80/3.6)^2/120
4938 N
which is applied horizontally at the center of mass

Since the center of mass is 0.650 m above the road surface, there is a moment arm. Assuming the car does not skid, this is a statics situation

Sum torque at the inner wheels
The distance from the contact patch of the wheels and the center of mass is
sqrt(0.65^2+0.8^2)
1.03 m





Summing torques:
4938*0.65+1200*9.81*0.80-Fo*1.6=0
solve for Fo, the force of the road reacting to the downward force of the outside wheels
7892 N

Now let's solve for Fi two ways to check the answer

Summing torques at the outside contact patch
1200*9.81*0.8-4938*0.65-Fi*1.6=0
solve for Fi
3880 N

The other method is to sum forces in the vertical

3880+7892-1200*9.81=0
0=0
It checks

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