Kinetic Energy including a pulley

[Lydia22]

Homework Statement

Two blocks, of masses M = 2.0 kg and 2M are connected to a spring of spring constant k = 200 N/m that has one end fixed, as shown in the figure below. The horizontal surface and the pulley are frictionless, and the pulley has a moment of inertia I=0.005 kg.m^2 with radius R=0.050 m. The blocks are released from rest with the spring relaxed.i.e in its equilibrium position).

(a) What is the combined(total) kinetic energy of the two blocks when the hanging two-block-pulley system has fallen a distance of 0.090 m?
J

(b) What is the rotational kinetic energy of the pulley when the hanging blockhas fallen 0.090 m?
http://www.webassign.net/hrw/W0155-N.jpg]2. Homework Equations [/b]
Mass 1
Fnet(X)= [T[/1] -[F][/sp] =[M][/1][a][/x]= [T][/1] -KΔs

Pulley
[T][/net] =[T][/1]R -[T][/2]R= -IΩ
Hanging Mass
[F][/net]=[M][/2]-[T][/2]=[M][/2]

The Attempt at a Solution

Three equations Four unknowns ,I do not know how to proceed from this point.

 

[tiny-tim]

Hi Lydia!

Why forces?

Just call the speed "v", and calculate all the energies.

 

[Lydia22]

I was trying to get the acceleration the lead to velocity

 

[tiny-tim]

i know!

you don't need to ​

 

[Lydia22]

If the velocity is final 'v'
K =0.5M[V][/2] + 0.5I[ω][/2] + 0.5{2M}[V][/2] + mgh
=0.5M[V][/2] + 0.5(0.5M[R][/2])[V][/2][R][/2] + 0.5{2M}[V][/2] - 2Mgh

 

[Lydia22]

But how do I know i don't need to? won't this be in terms of unknowns ?? #swimming in the pool of confused (EXAM in a few hours)

 

[tiny-tim]

(try using the X² button just above the Reply box )

If the velocity is final 'v'
K =0.5M[V][/2] + 0.5I[ω][/2] + 0.5{2M}[V][/2] + mgh
=0.5M[V]² + 0.5(0.5M[R]²)[V]²/[R]² + 0.5{2M}[V]² - 2Mgh

Yes, but

i] I is given in the question

ii] you've left out the springy part!

 

[Lydia22]

If the velocity is final 'v'
K =0.5M[V][/2] + 0.5I[ω][/2] + 0.5{2M}[V][/2] + mgh
=0.5M[V][/2] + 0.5(0.005[V][/2][0.050][/2] + 0.5{2M}[V][/2] - 2(9.8)(0.090) + 0.5(200)(ΔS)

 

[tiny-tim]

a bit difficult to read

i think it's ok, except that the spring KE should be 1/2 k h²

 

[Lydia22]

Sorry i cannot use those fancy buttons.Thank you for the little light