What will be the kinetic energy of pile driver ram when it undergoes a 10 kJ decrease in potential energy?

Question

What will be the kinetic energy of pile driver ram when it undergoes a 10 kJ decrease in potential energy?

Answer 1

Well, let's see.... E_pe= mgh  m=mass, g=9.80 m/s^2, h=height.   E_ke=.5*mv^2...  So,, we need to set up a situation where the inital is a variable, and the change of PE would cancel out the non-essential parts.  So, for E0=mgh=.5mv^2,,,  it seems like the reduction of 10kJ would equate to a loss of height.  Gravity does not change and the mass would not change.  Thus the only option left is for the height to change, and the velocity would be a function of height.  (2gh)^.5 = v(h)  So if you reduce the PE by 10kJ, then the KE reduces by 141 m/s, more or less.  I think that's right, I don't have a calculator, so my math might be off.