The photograph below shows a girl pushing on a large stone sphere. The sphere ha

Question

The photograph below shows a girl pushing on a large stone sphere. The sphere has a mass of 8200 kg and a radius of 90 cm and floats with nearly zero friction on a thin layer of pressurized water.

Suppose that she pushes on the sphere tangent to its surface with a steady force of F = 65 N and that the pressured water provides a frictionless support. How long will it take her to rotate the sphere one time, starting from rest?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

let I be the moment of inertia of the sphere = (2/5)*M*R^2 = (2/5)*8200*0.9^2 = 2656.8 kg -m^2

alpha is the angular accelaration

Torque T = I*alpha = F*R = 65*0.9 = 58.5

alpha = 58.5/(2656.8) = 0.022 rad/s^2

then using theta = 0.5*alpha*t^2

2*pi = 0.5*0.022*t^2

2*3.142 = 0.5*0.022*t^2

t = 24 sec

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.