# Work and change in kinetic energy

I know that the net work = the change in kinetic energy, delta KE. But what if the object has both the potential energy and kinetic energy, for example, a falling object, then how can I find out the work done on the object at a particular point? Still the change in KE ignore PE?
Also, I know the external work = the change in potential enery, delta PE. It happens in a lifting a brick, but Is that the net work? What's the difference? In addition, work done by gravity= -delta PE. If I am asked to find out the net work, should I plus together the external work and work done by gravity? In this lifting case, is there a kinetic energy? Can I find out the net work by using change in KE? I am confused with some concepts, hope you can help. thanks.

## Answers and Replies

what problem is this for?

no. there is no problem for this. I am just asking since I read the concepts in the book, but I have confusion.

jtbell
Mentor
The net work done by all forces acting on an object equals the change in the object's kinetic energy:

$$W_{net} = \Delta KE$$

Forces can be either conservative (that is, they have a potential energy associated with them) or non-conservative (that is, they don't have a potential energy associated with them). Therefore we can split the net work done by all forces into two parts correspondingly:

$$W_{net}^{(c)} + W_{net}^{(nc)} = \Delta KE$$

The work done by a conservative force equals the negative of the change in the potential energy associated with that force. (This is the definition of potential energy.) Adding up the effects of all the conservative forces:

$$W_{net}^{(c)} = - \Delta PE$$

Therefore the net work done by the non-conservative forces equals the change in the object's mechanical energy (sum of kinetic and potential energies):

$$W_{net}^{(nc)} = \Delta (KE+PE)$$

The net work done by all forces acting on an object equals the change in the object's kinetic energy:

$$W_{net} = \Delta KE$$

Forces can be either conservative (that is, they have a potential energy associated with them) or non-conservative (that is, they don't have a potential energy associated with them). Therefore we can split the net work done by all forces into two parts correspondingly:

$$W_{net}^{(c)} + W_{net}^{(nc)} = \Delta KE$$

The work done by a conservative force equals the negative of the change in the potential energy associated with that force. (This is the definition of potential energy.) Adding up the effects of all the conservative forces:

$$W_{net}^{(c)} = - \Delta PE$$

Therefore the net work done by the non-conservative forces equals the change in the object's mechanical energy (sum of kinetic and potential energies):

$$W_{net}^{(nc)} = \Delta (KE+PE)$$

thanks. If there is no non-conservative force in the system, then Wcnet=delta KE, then since Wcnet=-deltaPE, so now -deltaPE=delataKE? Either one works for the net work? Btw, as I said before, external work = the change in potential enery, delta PE. In addition, work done by gravity= -delta PE. One is positive delta PE, the other one is negative delta PE, why here Wcnet=-PE? Why we want the negative PE, but the positive one? because we want gravitational potential energy? acted by gravity?

Wexternal=delta PE, Wgravity=-delta PE. On my book, it says the change in potential energy associated with a particular force is equal to the negative of the work done by that force if the object is moved from one point to a second point. I think it indicates Wgravity=-deltaPE, but why must a change in potential energy relates to negative work done by a force not a positive work as in the external force's case?

I know that the net work = the change in kinetic energy, delta KE. But what if the object has both the potential energy and kinetic energy, for example, a falling object, then how can I find out the work done on the object at a particular point? Still the change in KE ignore PE?
Also, I know the external work = the change in potential enery, delta PE. It happens in a lifting a brick, but Is that the net work? What's the difference? In addition, work done by gravity= -delta PE. If I am asked to find out the net work, should I plus together the external work and work done by gravity? In this lifting case, is there a kinetic energy? Can I find out the net work by using change in KE? I am confused with some concepts, hope you can help. thanks.

You can draw a diagram showing 3 states - initial, falling and final. In the initial state, the object has maximum PE and zero KE since it's stationary. When it's in the falling state, maximum PE is slowly being converted into some KE. In the final state, assume the object stops upon hitting the ground, then all of its PE is converted into maximum KE just before it hits the ground.

You can draw a diagram showing 3 states - initial, falling and final. In the initial state, the object has maximum PE and zero KE since it's stationary. When it's in the falling state, maximum PE is slowly being converted into some KE. In the final state, assume the object stops upon hitting the ground, then all of its PE is converted into maximum KE just before it hits the ground.

I know. BUt how do you find the Net work/total work? Use delta KE? BTw, in the example that you were talking about, is there any work done by external force? like what does it really mean by external force? ex. a spring connected to a block, find the work done on the block. Then is there an external force? Why the block's energy changes so that I can not use the conservation of energy? I am seriously confused with external work delta PE or the work done by gravity -delta PE and net work?

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