What speed must a car travel over a hill to exert no force on the road?

[beckysamis]

Homework Statement

A 915kg car goes over a hill. If the radius of this curve is 43m, how fast must the car travel so that it exerts no force on the road at the crest.

Homework Equations

Fc = mv^2/r
Fg = mg

The Attempt at a Solution

Fc = Fn+Fg
Fn=Fg
Fg=mg
=(915)(9.81)
=8976.15
Fc=?

 

[Doc Al]

Fc = Fn+Fg

OK.

Fn=Fg

No. If there's no force on the road, what must Fn equal?

Fg=mg
=(915)(9.81)
=8976.15

OK.

 

[gdbb]

If the car must exert no force on the road at the crest, what does that say about the force the road must exert on the car at the crest? :)

 

[cupid.callin]

Fc = Fn+Fg

OK.

Should it be Fc = Fg - Fn ?

but yes anyway, it will give same result.

 

[rwisz]

To determine the speed needed for the car to exert no force on the road at the crest, we can use the equation Fc = mv^2/r. Since we want the net force to be zero, we can set Fc equal to zero and solve for v. This gives us the equation 0 = mv^2/r. We can then substitute in the known values of m (915kg) and r (43m) to get 0 = (915)(v^2)/43. Solving for v, we get v = √(43*0/915) = 0 m/s. This means that the car must be travelling at 0 m/s at the crest of the hill in order to exert no force on the road.