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

AI Thread Summary
To determine the speed at which a 915kg car must travel over a hill with a 43m radius to exert no force on the road, the centripetal force (Fc) must equal the gravitational force (Fg) acting on the car. The gravitational force is calculated as Fg = mg, resulting in approximately 8976.15 N. At the hill's crest, if the car exerts no force, the normal force (Fn) is zero, leading to the equation Fc = Fg. The discussion emphasizes that the car's speed must be sufficient to maintain this balance of forces without exerting any downward force on the road. Understanding these dynamics is crucial for solving the problem accurately.
beckysamis
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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=?
 
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beckysamis said:
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.
 
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? :)
 
Doc Al said:
beckysamis said:
Fc = Fn+Fg
OK.

Should it be Fc = Fg - Fn ?

but yes anyway, it will give same result.
 

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