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What is the speed? Lifesaver

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Question:

A car is coasting without friction toward a hill of height h and radius of curvature r. (a) What is the initial speed, Vo, will result in the car’s wheels just losing contact with the roadway as the car crests the hill? (b) What happens if the initial speed of the car is greater than the value found in part?

Answers:

Mystic Monkey

Oracle

Karma Points: 59,783

(NIMBLE - the National Institute of Monkey Business and Learning)

Date Posted: 6/18/2008 12:35:00 AM Status: Live

Asker's Rating: Lifesaver

Response:

circular motion: sum of vertical forces = mv²/r

mg - normal = mv² / r

just lose contact >> normal is zero

mg = mv² / r

v² = gr

This is the speed at the top of the hill. For the initial speed, use cons of energy

initial K + U = final K + U where final is at top of hill

(1/2) m v² + 0 = (1/2) m v² + m g h

v² = gr + 2 g h

v = [ g ( r + 2h) ]^1/2 this is the initial coasting speed of the car

(b) if car is moving faster than this, it will go "airborne" as it crests the hill

MaryCosSin's Comment:

excellent

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What is the speed? Lifesaver

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