a) What is the moment of inertia for the sphere? b) How far up the ramp, L , doe

Question

a) What is the moment of inertia for the sphere?

b) How far up the ramp, L, does the sphere go before it stops moving?

17. A solid spherical mass, M-5.00 kg and radius 15.0 cm, compresses a spring of spring constant is k = 2.00 105 N/m a total distance of 65.0 cm. The sphere is released from rest and is propelled up a ramp inclined at an angle of 20.0° with respect to the horizontal. There is friction between the sphere and the ramp. Assume that the coefficient of friction between the sphere and the ramp is .-0.500.

Explanation / Answer

(a)

moment of inertia I = (2/5)*M*R^2 = (2/5)*5*0.15^2 = 0.045 kg m^2

(b)

initial elastic potential energy stored Ui = (1/2)*k*x^2

work done by friction Wf = -uk*m*g*costheta*L

final gravitational potential energy Uf = m*g*L*sintheta

Ui + Wf = Uf

(1/2)*k*x^2 - uk*m*g*costheta*L = m*g*L*sintheta

(1/2)*2*10^5*0.65^2 - (0.5*5*9.8*cos20*L) = 5*9.8*L*sin20

L = 1062 m

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