"The drawing shows a version of the loop-the-loop..." was answered by our community

ddaeeric

Answered question

2020-11-20

The drawing shows a version of the loop-the-loop trick for a small car. If the car is given an initial speed of 4 m/s, what is the largest value that the radius r can have if the car is to remain in contact with the circular track at all times?

Answer & Explanation

Sadie Eaton

Skilled2020-11-21Added 104 answers

At the top of the loop the gravitational force provides the centripetal force for the car
to remain in the loop, so

m \cdot g = m \cdot \frac{v^{2}}{R}

and

R = \frac{v^{2}}{g}

. Any larger radius of the loop
will require a corresponding increase speed of the car to remain in contact with the loop. At
any other position in the loop the normal force of the track on the car plus the gravitational
component of the force in the radial direction provides the centripetal acceleration. For instance
at the bottom of the loop

N - m g = m \cdot \frac{v^{2}}{R}

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