A physics major is working to pay his college tuition by performing in a traveli

Question

A physics major is working to pay his college tuition by performing in a traveling carnival. He rides a motorcycle inside a hollow transparent plastic sphere. After gaining sufficient speed, he travels in a vertical circle with a radius of 13.4 m . The physics major has a mass of 72.0 kg , and his motorcycle has a mass of 40.0 kg.

FIND

A) What minimum speed must he have at the top of the circle if the tires of the motorcycle are not to lose contact with the sphere?

B) At the bottom of the circle his speed is twice the value calculated in part A. What is the magnitude of the normal force exerted on the motorcycle by the sphere at this point?

Explanation / Answer

(a)

At top of the circle,

Centripetal force = gravitational force

Let, minimum speed = v

mv^2 / r = mg

v^2 / r = g

v = sqrt (rg)

v = 11.45 m/s

(b)

At bottom of circle,

v' = 2v

centripetal acceleration, ac = v'^2 / r = (2v)^2 / r

ac = 4* (v^2 / r) = 4g

Net force, N - mg = m*ac

N / m = ac + g = 5g

N = 5mg

N = 5*(72 + 40)*9.8

N = 5488 N

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