From: rlamont at POSTOFFICE.PROVIDENCE.EDU (Bob LaMontagne)
Date: Wed Aug 17 19:12:48 2005
Since I have been rather fussy about what solutions I would accept to the
question of how do you find the speed of a falling ball after 5 seconds only
using energy, let me propose a solution that I think is acceptable.
mgh + 0.5 m v^2 = constant
Take the derivative of the above.
mg (dh/dt) + m v (dv/dt) = 0
v = - dh/dt
- mgv + mv (dv/dt) = 0
Therefore
dv/dt = g
And
v = gt
So v = 50 after 5 seconds.
M and g are just numbers. (I really don't understand what m means in this
case, or what sets the value of g). But at least there is no overt appeal to
kinematics. There is an implicit one by assuming g = 9.8 :-(
I see this derivation as a correct solution, but there is no way I would
present this to students as a way of understanding free fall motion.