Solve Using Conservation of Energy

• joemama69

Homework Statement

Solve Using Conservation of Energy

The spool has a mas of 50 kg and a radius of gyration k(o) = .280m. If the 20 kg block A is released form rest, determine the distance the block must fall in order for the spool to have an angular velocity w = 5 rad/s. Also what is the tension in the cord while the block is in motion? Neglect the mass of the cord

The Attempt at a Solution

T1 + V1 + T2 + V2

Does V1 = 0 because it is at rest from the start

T1 = .5mv2 + .5Iw2 = .5*20*0 + .5*50*.282 = 1.96

V2g = Wy (y is what I am looking for but how do i calculate work W)
V2e = .5ks2 = .5*.28*s2 = .14s2

T2 = .5*20*v2 + .5*50*.282 = 10v2 + 1.96

1.96 = Wy + .14s2 + 10v2 + 1.96

To answer the question "determine the distanc ethe block must fall" means solve for y right

To answer the question "what is the tension of the cord" means solve for s right

How do i find v

The distance the block falls is your energy..

What does that go into?

m_b*g*h = 1/2*m_b*V2 + 1/2*m_s*R_s22

V = ω*R_s

So h is what you are solving for and I think that looks like ...

h = 1/2*ω2R_s2*(m_b + m_s)/(g*m_b)