Uniform Circular Motion on a racetrack

Thread starter cle102
Start date Nov 29, 2020
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Circular Circular motion Motion Uniform Uniform circular motion

1 reply · 2K views · last reply Nov 29, 2020

cle102

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Nov 29, 2020

Homework Statement: A racetrack has the shape of an inverted cone, as the drawing shows. On this surface the cars race in circles that are parallel to the ground. For a speed of 34.0 m/s, at what value of the distance d should a driver locate his car if he wishes to stay on a circular path without depending on friction?

Relevant Equations: a=v^2/R
F꜀=(mv^2)/R
μg = v^2/R

Diagram of a conical funnel with a dashed vertical axis, showing a small object moving in a horizontal circle on the inner conical surface, with radius labelled d and the cone's sides at 40.0 degrees to the horizontal on each side.

Not sure what I'm doing here. Not sure how to continue? Please help.

Handwritten derivation of radius R from Newton's second law for circular motion: sum of F = mv^2/R, then -mg + mg/sin40 = mv^2/R, then 0.55572g = v^2/R, 5.44609 = 34^2/R, and R = 212.26224.

Thank you in advance!

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kuruman

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Nov 29, 2020

First solve the other problem you posted, and you will see how to approach this one. The strategy is the same, only the unknown quantities are different.

Uniform Circular Motion on a racetrack

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