Question

(11 %) Problem 7: An object rolls without slipping down a 2.01 m high incline. Randomized Variables d 2.01 m v 5.8 m/s What is the moment of inertia of the object starting from rest if it has a final velocity of 5.8 m/s? Express the moment of inertia as a multiple of MR2, where M is the mass of the object and R is its radius. Grade Summary Deductions Potential Late Work % 75% 0% 400%

Answer 1

on the incline initial energy Ei = M*g*d

at the bottom , final energy Ef = (1/2)*M*v^2 + (1/2)*I*w^2

w = angular speed = v/R

Ef = (1/2)*M*v^2 + (1/2)*I*(v/R)^2

Ef = (1/2)*M*v^2 + (1/2)*I*v^2/R^2

from energy conservation

total energy is conserved

Ef = Ei

(1/2)*M*v^2 + (1/2)*I*v^2/R^2 = M*g*d

(1/2)*I*v^2/R^2 = M*g*d - (1/2)*M*v^2

(1/2)*I*v^2/R^2 = M(g*d - (1/2)*v^2)

I/MR^2 = 2*g*d/v^2 - 1

I/(MR^2) = 2*9.81*2.01/5.8^2 - 1

I/MR^2 = 0.172