Homework Answers
let v is the linear speed and w is the angular speed of
sphere at the bottom of the ramp.
Apply conservation of energy
final kinetic energy = initial potential energy
(1/2)*m*v^2 + (1/2)*I*w^2 = m*g*h
(1/2)*m*v^2 + (1/2)*(2/5)m*r^2*w^2 = m*g*h
(1/2)*m*v^2 + (1/5)*m*(r*w)^2 = m*g*h
(1/2)*m*v^2 + (1/5)*m*v^2 = m*g*h
(7/10)m*v^2 = m*g*h
v = sqrt(10*g*h/7)
now, y_max = v^2/(2*g)
= (10*g*h/7)/(2*g)
= (5/7)*h <<<<<<<<---------------Answer
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