physics question about work and potential energy. MIDTERM TONIGHT?

Question

One of the examples in my notes states: Dr. D who has a mass of m=68kg easts a 300 Cal candy bar and then climbs 10 stories (Delta h= 35 meters) to his office. How many Calories has he burned?

so Work done = the change of PE (potential energy) = mgh= (68kg)(9.8 m/s^2) (35m) = 23300 J x (1Cal/ 4186 J)= 5.6 Cal

I understand the process of how they get 5.6 Cal but what I don't understand is why they used Word done= the change of PE? I thought Work was = the change of KE (kenetic engery)? isnt potential energy defined as stored energy associated w/position or configuration? or is the potential energy actually stored in Dr. D himself? and KE is derived from a veloctiy acting on a system?? please help explain this!!!

Answer 1

Good question.

We can write energy conservation as

work done + potential energy + kinetic energy +...= total energy of the at any time

As Dr. D of mass m climbs his potential energy is increase by work done. So we can say Dr. D is to climb height h at any time its position d we would have
work climbing +Pe = Pemax or
mg d + mg(h-d)= mg h Does that make sense? To make sense teh equation must balance
mg d + mg(h-d)= mg h
mg d + mgh- mg d= mg h
mg h= mg h !

If Dr D is to fall distance a

Pe1 + Ke1=Pe(max)
mg(h-d) + 0.5mV^2 = mgh
d=0.5gt^2
V=gt
mg(h-0.5gt^2) + 0.5m(gt)^2 = mgh
do a little algebra and see that energy equation is balanced

Answer 2

In order to understand this problem you have to understand that potential energy is measured in a relative sense in a lot of cases. In this case you can assign 0 potential energy to the point where the ball would reach the lowest point, so in the first case the ground and in the second case the bottom of the well. From there you can apply P = mgh to determine the potential energy.