# Change in Potential energy equals change in Kinetic energy?

EMdrive

## Homework Statement

I'm trying to digest the concept of change in potential energy being set equal to a change in kinetic energy. Does this relationship always hold? Please see below for more details.

PE = mgh
KE = .5mv^2
W = ΔKE = -ΔPE
W = f*d

## The Attempt at a Solution

[/B]
Lets say I have a block that is being pushed up an incline at constant velocity by a force F for a distance d. Because the velocity is constant, it follows that the net force on the object is 0, and therefore the total work done on the object should also be 0. This is further explained by the W = ΔKE equation in which the final and initial kinetic energies are the same, resulting in a work of 0 J. However, what baffles me is that while kinetic energy is clearly not changing, the potential energy is (height of the object is increasing). So the relationship W = ΔKE = -ΔPE does not hold because change in potential energy is some non-zero value... Can someone explain?

## Homework Statement

I'm trying to digest the concept of change in potential energy being set equal to a change in kinetic energy. Does this relationship always hold? Please see below for more details.

PE = mgh
KE = .5mv^2
W = ΔKE = -ΔPE
W = f*d

## The Attempt at a Solution

[/B]
Lets say I have a block that is being pushed up an incline at constant velocity by a force F for a distance d. Because the velocity is constant, it follows that the net force on the object is 0, and therefore the total work done on the object should also be 0. This is further explained by the W = ΔKE equation in which the final and initial kinetic energies are the same, resulting in a work of 0 J. However, what baffles me is that while kinetic energy is clearly not changing, the potential energy is (height of the object is increasing). So the relationship W = ΔKE = -ΔPE does not hold because change in potential energy is some non-zero value... Can someone explain?

Net work done is zero .Work done by gravity is non zero . PE is negative of work done by gravity .Hence PE is non zero .

Total mechanical energy is not conserved in this case .

• EMdrive
EMdrive
I see, that explains it. So the equation W = ΔKE = -ΔPE only applies in situations where total mechanical energy is conserved, which is not the case here (mechanical energy should be increasing here, correct?). But, just trying to understand, work can be 0 and the total mechanical energy of the system can still increase?

I just noticed it is your first post .

Welcome to PF !

I see, that explains it. So the equation W = ΔKE = -ΔPE only applies in situations where total mechanical energy is conserved, which is not the case here (mechanical energy should be increasing here, correct?). But, just trying to understand, work can be 0 and the total mechanical energy of the system can still increase?

W = ΔKE is Work Kinetic Energy theorem .W is net work done on the particle .This can further be written as Wnc + Wc =ΔKE . Wnc is work done by non conservative forces ( in your example it is work done by external agent pushing the block up .Wc is work done by conservative force ( in your example it is work done by gravity ) .

Now if you write Wc as -∆PE , Work KE theorem can be rewritten as ∆KE+∆PE = Wnc . This is the complete relation .It also applies in your case .In your example ,since Wnc ≠0 , ∆KE+∆PE ≠ 0 .

In your example net work done W = 0 . ∆KE+∆PE = Work done by external agent (whosoever is pushing the block up )

∆KE+∆PE = 0 only when conservative forces are acting .Here the force exerted by agent pushing the block up is a non conservative force .

Hence correct relation to use in your example is ∆KE+∆PE = Wnc .

Last edited:
• EMdrive and TSny
TSny
Homework Helper
Gold Member
As @conscience explained, ∆KE= -∆PE for systems in which the following is true:

(1) no external work is done on the system (e.g., system is "isoloated")

(2) internal work is done by conservative forces only (like gravity or springs).

For a modern video on this concept using fancy, mind-blowing graphics, see

• conscience and EMdrive
EMdrive
I just noticed it is your first post .

Welcome to PF !

W = ΔKE is Work Kinetic Energy theorem .W is net work done on the particle .This can further be written as Wnc + Wc =ΔKE . Wnc is work done by non conservative forces ( in your example it is work done by external agent pushing the block up .Wc is work done by conservative force ( in your example it is work done by gravity ) .

Now if you write Wc as -∆PE , Work KE theorem can be rewritten as ∆KE+∆PE = Wnc . This is the complete relation .It also applies in your case .In your example ,since Wnc ≠0 , ∆KE+∆PE ≠ 0 .

In your example net work done W = 0 . ∆KE+∆PE = Work done by external agent (whosoever is pushing the block up )

∆KE+∆PE = 0 only when conservative forces are acting .Here the force exerted by agent pushing the block up is a non conservative force .

Hence correct relation to use in your example is ∆KE+∆PE = Wnc .

Thank you so much for the concise and complete explanation. It finally makes sense now! I really appreciate the help :)