How to Calculate Work on a Puck Using Conservation of Angular Momentum?

[riseofphoenix]

Determining the work done on the puck using conservation of angular momentum?? Help!

This is what I did...

1) Given

m_puck = 0.300 kg
r_initial = 0.4 m
v_initial = 0.6 m/s

m_puck = 0.300 kg
r_final = 0.15 m
v_final = ____ m/s

ƩW = KE_final - KE_initial

2) KE_initial = (1/2)mv²
KE_initial = (1/2)(0.300)(0.6²)
KE_initial = 0.054 J

3) KE_initial = (1/2)mv²
KE_initial = (1/2)(0.300)v²
KE_initial = 0.15v²

4) Find v - Angular momentum is conserved due to a lack of friction. The puck goes from 40 cm to 15 cm, so it has a different angular momentum.

L_initial = L_final
Iω_initial = Iω_final
[STRIKE](0.300)[/STRIKE](0.4)(0.6)² = [STRIKE](0.300)[/STRIKE](0.15)v²
(0.4)(0.6)² = (0.15)v²
0.144/0.15 = v²
0.96 = v²
0.979 = v

5) Plug v back into Net work equation

ƩW = KE_final - KE_initial
ƩW = (0.979) - (0.054)
ƩW = 0.925 J

Which is wrong...
:(
Help!

 

[TSny]

L_initial = L_final
Iω_initial = Iω_final
[STRIKE](0.300)[/STRIKE](0.4)(0.6)² = [STRIKE](0.300)[/STRIKE](0.15)v²

You want those squares?

 

[riseofphoenix]

You want those squares?

Oh...

But even without them I still get the wrong answer.


(0.4)(0.6) = (0.15)v_final

1.6 = v_final

4) KE_final = 0.15(1.6²)
KE_final = 0.15(2.56)
KE_final = 0.384

So,

W = (0.384) - (0.054) = 0.33

Still wrong...

 

[riseofphoenix]

brb in an hour!

 

[TSny]

(0.4)(0.6) = (0.15)v_final

Is 0.15 m correct for the final radius? Another reading of the question might help.

 

[riseofphoenix]

Is 0.15 m correct for the final radius? Another reading of the question might help.

Final radius would be... .4 m - .15 = .25!

Ohhhhh thank you!