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

Homework Equations

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

V_2g = Wy (y is what I am looking for but how do i calculate work W)
V_2e = .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

 

[LowlyPion]

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_s²*ω²

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)