Momentum is Potential Energy?

In summary, the derivative of potential energy with respect to time is force, while the derivative of momentum with respect to time is also force. However, momentum and potential energy are not equivalent and do not have a simple connection. Work can be calculated by integrating force with respect to distance or by finding the time rate of change of work, but it is not accurate to say "work in respects to distance". Instead, we can say that work is a function of both coordinate and time, and can be calculated by integrating force with respect to distance or by finding the negative derivative of potential energy with respect to distance.
  • #1
UrbanXrisis
1,196
1
the derivative of potential energy (inrespects to time) is Force right?

F=-dPE/dt

I also read that the derivative of momentum (inrespects to time) is force.

F=dp/dt

Can I conclude that momentum is Potential Energy?

p=-PE
 
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  • #2
UrbanXrisis said:
the derivative of potential energy (inrespects to time) is Force right?

F=-dPE/dt
No. This is incorrect. Force is the space derivative of Work or Energy.: F = dW/dx
This is more often seen as Force x distance = work or: dW=Fdx

A good example of this is gravity: PE = mgh. dPE/dh = mg which of couse is the force due to gravity.

dPE/dt = dW/dt = Power or the time rate at which work is done


AM
 
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  • #3
Okay, let me restate then...

the integral of force (inrespects to time) is Impulse right?

∫F=Impulse=p(t)

the derivative of Potential Energy (inrespects to distance) is Force right?

PE'(x)=F(x)


is this correct?
 
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  • #4
Is it true that work in respects to time is the same as the negative Potential Energy?

w(t)=-PE(t)

Is it true that work in respects to distance is the same as the negative Potential Energy?

w(x)=-PE(x)
 
  • #5
UrbanXrisis said:
Okay, let me restate then...
the integral of force (inrespects to time) is Impulse right?
∫F=Impulse=p(t)
the derivative of Potential Energy (inrespects to time) is Force right?
PE'(t)=F(t)
Then Impulse = PE?

I believe that Andrew was more than clear.The force is the gradient of the potential energy,which involves DERIVATIVES WRT TO SPACE COORDINATES AND NOT WRT TO TIME...So there is no simple connection between momentum and potential energy.To give a clear and hopefully comprehedable example:an apple in a tree has momentum zero (it's speed is zero,as long as the wind's not blowing),but has a potential energy 'mgh',where 'm' is its mass,'g' is the acceleration due to gravity and 'h' is the height above the ground assumed the level with 0 gravitational potential energy.

Daniel.
 
  • #6
dextercioby said:
I believe that Andrew was more than clear.The force is the gradient of the potential energy,which involves DERIVATIVES WRT TO SPACE COORDINATES AND NOT WRT TO TIME...So there is no simple connection between momentum and potential energy.To give a clear and hopefully comprehedable example:an apple in a tree has momentum zero (it's speed is zero,as long as the wind's not blowing),but has a potential energy 'mgh',where 'm' is its mass,'g' is the acceleration due to gravity and 'h' is the height above the ground assumed the level with 0 gravitational potential energy.

Daniel.

Yeah, I sort of realized that. It's changed
 
  • #7
UrbanXrisis said:
Is it true that work in respects to time is the same as the negative Potential Energy?

w(t)=-PE(t)

Is it true that work in respects to distance is the same as the negative Potential Energy?

w(x)=-PE(x)

What do you mean "work in respects to distance".Work is a physical quantity and mathematically it is function which can depend both on the coordinate and time.You might have meant:
[tex] W(x,t)=-E_{pot} (x,t) [/tex] (1)
Compare the definitions and tell me whether (1) is correct:
[tex] W(x,t)=\int F(x,t) dx [/tex] (2)
[tex] F(x,t)=-\frac{dE_{pot}(x,t)}{dx} [/tex](3)

I guess it is.But it's not fair to break the functional dependence and state "work in respects to distance".

Daniel.
 
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  • #8
I know the integral of force in respects to distance is w(x).
I know that the integral power in respects to time is w(t).

I assumed that w(x)=delta KE(x) = -PE(x)
and that w(t)=delta KE(t) = -PE(t)
 

1. How is momentum related to potential energy?

Momentum is a measure of an object's mass and velocity, while potential energy is a measure of an object's position and its ability to do work. Therefore, the two are related because an object with momentum has the potential to do work.

2. Can an object have momentum without having potential energy?

Yes, an object can have momentum without having potential energy. This can occur when an object is in motion in a straight line, without any changes in elevation or position.

3. How does the conservation of momentum relate to potential energy?

The conservation of momentum states that the total momentum of a system remains constant, unless acted upon by external forces. This also means that the total potential energy of a system will remain constant, as the two are directly related.

4. How does momentum affect an object's potential energy?

Momentum does not directly affect an object's potential energy. However, an object's momentum can be converted into potential energy through changes in its position or elevation, such as in the case of a roller coaster or a pendulum.

5. Is momentum the same as kinetic energy?

No, momentum and kinetic energy are not the same. Kinetic energy is a measure of an object's motion, while momentum is a measure of its mass and velocity. However, both can be related to an object's potential energy, as they both contribute to an object's ability to do work.

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