A car has a mass of 1500 kg and travels with a speed of 5 m/s. The car passes over the top of a convex bridge that has a radius of curvature equal to 10 m. What is the force of the bridge on the car as it passes over the top?

###### Solution.

According to Newton’s Second Law for uniform circular motion, the net force acting on the car equals ma_{r}.

F_{net} = ma_{r}

The expression F_{net} = ma_{r} is a vector equation.

In the y-direction, there are only F_{N} and mg.

The positive y-axis is directed toward the center of curvature.

Thus,

mg – F_{N} = ma_{r} (1)

We know that a_{r} = v^{2}/r, then we can rewrite the equation (1) as

mg – F_{N} = mv^{2}/r

or

F_{N} = mg – mv^{2}/r

F_{N} = m(g – v^{2}/r)

We substitute the values and we get

F_{N} = 1500(9.8 – 5^{2}/10) = 10950 N