Why Do Terms in the Energy Equation Not Cancel as Expected?

  • #1
2much
14
0
I have an equation relating potential energy1 plus gravitational energy1 = potential energy2 plus gravitational energy2

1/2 mv21 + mg1 = 1/2 mv22 + mg2

Now cancelling out the terms I have

v21 + 2gy1 + v22 2gy2

Now I don't understand why mg in the second term of both expressions don't cancel out. Why are we left with 2gy, not just y
 
Physics news on Phys.org
  • #2
First of all, note that gravitational energy is mgh, mg is just the force.
So you presumably meant

1/2 m v1² + mgy1= 1/2 m v2² + mgy2

Then you can multiply by 2 and divide it by m, but of course then you have to multiply everything, which gives

2/m(1/2 m v1² + mgy1) = 2/m (1/2 m v1²) + 2/m (mgy1) = v1² + 2gy1.
The 2 and 1/2 cancel out in the first term, and the m cancels out in both terms, but you have to leave the rest.
The right hand side is similar.
 
Back
Top