When timmy is sitting at rest he have 40j of GPE then his dad gives timmy a big push when his dad let go timmy has 60j of GPE and 120j KE. How much work did timmy dad do when he pushed timmy?

To find out how much work Timmy's dad did when he pushed him, we can use the Work-Energy Principle, which states that the work done on an object is equal to the change in its total mechanical energy.

In this case, the change in Timmy's total mechanical energy is the difference between his initial gravitational potential energy (GPE) and his final total mechanical energy.

Initial GPE = 40 J
Final GPE = 60 J
Final KE = 120 J

Total Mechanical Energy = GPE + KE

Initially:
Total Mechanical Energy = Initial GPE + 0 (since Timmy is at rest)

Finally:
Total Mechanical Energy = Final GPE + Final KE

Now we can calculate the change in total mechanical energy:

Change in Total Mechanical Energy = (Final GPE + Final KE) - (Initial GPE + 0)

Change in Total Mechanical Energy = (60 J + 120 J) - 40 J

Change in Total Mechanical Energy = 180 J - 40 J

Change in Total Mechanical Energy = 140 J

Therefore, the work done by Timmy's dad when he pushed Timmy is equal to the change in total mechanical energy, which is 140 J.