Energy Required to Lift an Object to Various Heights

[harveydinkle]

Homework Statement

Consider a ball of m = 0.50kg. Does it take the same amount of additional energy to vertically lift it from 15cm to 25cm as it does to lift it from 25cm to 35cm? If not, which takes more? Why?

Homework Equations

Potential energy: mgh
Work = Kf - Ki

The Attempt at a Solution

I believe that the energy required in both scenarios should be equal, as the work done is the same in each case.

Starting at 15cm and going to 25cm, the potential energies in each position respectively are
0.5kg*9.8m/s²*0.15m = 0.735J
0.5kg*9.8m/s²*0.25m = 1.225J
A difference of 0.49J

Starting at 25cm and going to 35cm...
0.5kg*9.8m/s²*0.25m = 1.225J
0.5kg*9.8m/s²*0.35m = 1.715J
A difference of 0.49J

The differences between the final and initial potential energies are equal, but are the differences the value of interest? Is the energy to lift the box equal to the difference in potential energy?

 

[TomHart]

Welcome to Physics Forums.
I think you got it right.

 

[CWatters]

I agree. You could argue that g isn't constant with height but the difference is negligible in this case.