Natural force of circular motion

[peweee17]

Homework Statement

A 950kg sports car (including driver) crosses the rounded top of a hill (radius = 86.0m) at 10.0m/s.

Homework Equations

A. Determine the normal force exerted by the road on the car.
B. Determine the normal force exerted by the car on the 73.0kg driver.
C. Determine the car speed at which the normal force on the driver equals zero.

The Attempt at a Solution

I started to look at this problem like a loop da loop problem where there are different values of forces depeding on wether your on the top or bottom. Fn top= mg(((v^2)/rg)-1)

 

[cristo]

You need to show some work before we can help you, as per forum rules: what have you tried?

 

[baba89]

I would approach this problem by first identifying the natural force at play in this scenario, which is the centripetal force. This is the force that keeps an object moving in a circular path. In this case, the centripetal force is provided by the normal force exerted by the road on the car and the car on the driver.

To determine the normal force exerted by the road on the car, I would use the equation Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the car and driver, v is the velocity, and r is the radius of the hill. Plugging in the values given in the problem, I would get Fc = (950kg)(10.0m/s)^2/(86.0m) = 1105.81 N.

To determine the normal force exerted by the car on the driver, I would use the equation Fn = mg, where Fn is the normal force, m is the mass of the driver, and g is the acceleration due to gravity. Plugging in the values given in the problem, I would get Fn = (73.0kg)(9.8m/s^2) = 715.4 N.

To determine the car speed at which the normal force on the driver equals zero, I would set Fn = 0 in the equation Fn = mg and solve for v. This would give me v = √(rg), where r is the radius of the hill and g is the acceleration due to gravity. Plugging in the given values, I would get v = √((86.0m)(9.8m/s^2)) = 29.4 m/s.

In conclusion, the natural force of circular motion in this scenario is the centripetal force, which is provided by the normal force exerted by the road on the car and the car on the driver. The normal force exerted by the road on the car is 1105.81 N, and the normal force exerted by the car on the driver is 715.4 N. The car speed at which the normal force on the driver equals zero is 29.4 m/s.