Change in Kinetic & Potential Energy: Is KEf-KEi = PEf-PEi?

[username*]

if change in potential energy = change in kinetic energy the formula is

PEi + KEi = PEf +KEf

but change in kinetic energy by itself is: KEf- KEi

and change in potential energy is: PEf-PEi

so should change in potential energy = change in kinetic energy therefore be

KEf-KEi = PEf-PEi ?

I was looking at some questions and they were done differently...

My thinking is that it should be the first one--right?

 

[cristo]

This is a very random question, since you give no circumstances behind the question. However, its in intro physics so I'm going to take a guess.

Your first equation does not say that change in potential energy is equal to change in kinetic energy: rather it says that the sum of the potential and kinetic energy for a system at two different occasions is equal-- i.e. the total energy of a system is conserved. This is true for all closed systems.

For example, consider a ball rolling down a slope from rest, ignoring resistance. At the top of the ramp, the ball has a value of potential energy, call it V_i and zero kinetic energy. Thus V_i is the total energy of this system. If we then let the ball roll down the slope, halfway down it will have some potential and some kinetic energy: call these V_1 and K_1, respectively. Now, from conservation of energy, we know that V_1+K_1=V_i. Finally, when the ball reaches the bottom of the slope, all its energy is kinetic, K_f. Again, due to conservation of energy we obtain K_f=V_i.

So, we see that the first equation you cite is correct.

 

[rootX]

if change in potential energy = change in kinetic energy the formula is

PEi + KEi = PEf +KEf

I guess you are wrong there..
that equations means that total mechanical energy is constant
at certain given time Eti=PEi+KEi

so at another time
Etf=PEf+KEf

but Etf=Eti (constant)..

 

[cristo]

I guess you are wrong there..
that equations means that total mechanical energy is constant
at certain given time Eti=PEi+KEi

so at another time
Etf=PEf+KEf

but Etf=Eti (constant)..

Hmm.. I suppose that's not what I wrote in my post is it?