Driving in your car with a constant speed of v=13.0 m/s, you encounter a bump in the road that has a circular cross section. If the radius of curvature of the bump is r=33.2 m, calculate the force the car sear exerts on a 72.7 kg person as the car passes over the top of the bump.

No clue...

When the car is over the top of the bump it is accelerating downward. The acceleration is

a = v^2/r = (13 m/s)^2/(33.2 m)
= 5.09 m/s^2

72.7 kg person is thus accelerated downward at this acceleration.

Newton's second law says that:

F = m a

Let'S apply this to the person. There are two forces that act on the person. There is the gravitational force exerted by the entire Earth on the person. This force is directed downward and has a magnitude of:

F_g = 72.7 kg * g = 713 N

And there is the foce exerted by the chair F_ch

If the take the downward direction to be positive, we have:

(F_g + F_ch) = 72.7 kg * 5.09 m/s^2 --->

F_ch = -343 N

The minus sign means that it is directed upward.

To calculate the force the car seat exerts on a person as the car passes over the top of the bump, we can make use of the centripetal force formula.

The centripetal force can be defined as the force required to keep an object moving in a curved path, directed towards the center of the circle. In this case, the circular path is created by the bump in the road.

The formula for centripetal force is:

F = (m * v^2) / r

Where:
F is the centripetal force,
m is the mass of the person (72.7 kg),
v is the velocity of the car (13.0 m/s),
r is the radius of curvature of the bump (33.2 m).

Now, let's substitute the given values into the formula to calculate the force:

F = (72.7 kg * (13.0 m/s)^2) / 33.2 m

First, we square the velocity:
(13.0 m/s)^2 = 169.0 m^2/s^2

Next, we substitute the square of the velocity and the given values into the formula:

F = (72.7 kg * 169.0 m^2/s^2) / 33.2 m

Calculating further:

F = (12293.3 kg*m^2/s^2) / 33.2 m

F ≈ 370.73 N

Therefore, the force the car seat exerts on the 72.7 kg person as the car passes over the top of the bump is approximately 370.73 Newtons.