Question

A kugel fountain, also known as a floating sphere fountain, is a sculpture that suspends a large, typically stone, sphere on a thin plane of water. One of three in Columbus, is on campus in the Chadwick Arboretum on the corner of Lane Ave. and Olentangy. Kugel fountains have very little friction between the stone sphere and the hollow in which they sit, so it takes very little torque to start one moving from rest.

Required:
a. The kugel fountain in the Richard and Annette Bloch Cancer Survivor's Plaza in the Lane Ave Gardens has a granite sphere with a mass of approximately 1,800 kg, and a radius of about half a meter. You use your hand to apply a tangential force on the sphere to start it rotating from rest, and it takes 12 seconds to complete a quarter revolution. What is the average torque you applied to the sphere?
b. What is the average magnitude of the tangential force you applied?
c. How does this compare to the weight of a cellphone?

Answer 1

Step-by-step explanation:

Moment of inertia of sphere I = 2 /5 x m R²

m is mass and R is radius of the sphere .

I = 2/5 x 1800 x 0.5²

= 180 kg m².

For rotational motion starting from rest

θ = 1/2 α t²

Here θ = π /2 = 1.57 radians

t = 12 s

1.57 radians = 1/2 x α x 12²

Angular acceleration α = .022 rad /s²

Torque applied = I α

= 180 kg m² x .022 rad /s²

= 3.96 N.m

b ) Torque = F x r

F = Torque / r

= 3.96 / .5 = 7.92 N .

c )

Average weight of a cellophone is 1.3 N .

So the force applied is a little more than weight of a cellophone.