What Forces Act on a Car at the Peak of a Hill?

[pippintook]

A 1000 kg car traveling on a road that runs straight up a hill reaches the rounded crest at 25 m/s. If the hill at that point has a radius of curvature of - in a vertical plane - 75 m, what is the net downward force acting on the car at the instant it is horizontal at the very peak? How fast must the car go in order to leave the ground?


Honestly, I'm not even sure how to get started. I'm looking for F_N and the car's velocity, but I have no idea what the first step should be. Help please?

 

[PhanthomJay]

A 1000 kg car traveling on a road that runs straight up a hill reaches the rounded crest at 25 m/s. If the hill at that point has a radius of curvature of - in a vertical plane - 75 m, what is the net downward force acting on the car at the instant it is horizontal at the very peak? How fast must the car go in order to leave the ground?


Honestly, I'm not even sure how to get started. I'm looking for F_N and the car's velocity, but I have no idea what the first step should be. Help please?

Part 1: Draw a free body diagram of the car when it is at the top of the crest, and identify the forces acting on it (there are just 2 forces acting in the vertical direction). The net sum of these 2 forces is the centripetal force acting on it. you know v, so just calculate F_centripetal. Part 2: When the car leaves the ground, what is the Normal force acting on it? Then solve for v using the centripetal force equation per Newton 2.