Is the conservation of energy being applied correctly in this scenario?

[Kuklinski]

I don't know if I'm setting up the energies correctly.

1. Two objects are connected by a light string passing over a light, frictionless pulley. The object of mass m₁=5.00kg is released from rest at a height h=4m above the table. Using the isolated system model, (a) determine the speed of the object of mass m₂=3.00kg just as the 5.00-kg object hits the table and (b) find the maximum height above the table which the 3.00-kg object rises.
2. E₁=E_f
KE=.5mv²
U=mgh
3. E_i=E_f
m₁gh=m₂gh + .5(m₁+m₂)v²
5(9.8)(4) = 3(9.8)(4) + .5(8)(v²
v=4.43m/s

 

[tiny-tim]

Welcome to PF!

Hi Kuklinski! Welcome to PF!

Two objects are connected by a light string passing over a light, frictionless pulley. The object of mass m₁=5.00kg is released from rest at a height h=4m above the table. Using the isolated system model, (a) determine the speed of the object of mass m₂=3.00kg just as the 5.00-kg object hits the table and (b) find the maximum height above the table which the 3.00-kg object rises.

E_i=E_f
m₁gh=m₂gh + .5(m₁+m₂)v²
5(9.8)(4) = 3(9.8)(4) + .5(8)(v²
v=4.43m/s

Yes, that looks fine.

What's worrying you about it? ​