Energy conservative (Kinetic Energy and Potential Energy)

In summary: So remember that Wnc = 0 for conservative forces, and PhanthomJay's equation applies for all cases whether there are conservative forces or not.In summary, the conversation discusses how to compute an energy conservative equation for a given scenario where a book is being lifted with a constant velocity. It is mentioned that for the conservation of total energy, the work done by non-conservative forces is equal to the change in potential energy plus the change in kinetic energy. It is also clarified that this equation is only valid for an isolated system with no external forces, except for the gravitational force. The concept of work done by different types of forces is also discussed, with a reminder to always consider the gain and loss of energy. Lastly, the
  • #1
MechaMZ
128
0

Homework Statement


May i know how do i compute an energy conservative equation for the scenario below, which i don't understand.

If a book is lifted up by a force in order to make it moving upward with a constant velocity.
For conservation of total energy, W1-2 = U1-U2 = K2 - K1
If the object is moving in a constant velocity, isn't K2 - K1 = 0
However, U1 is not equal to U2.

It seems not correct obviously, hope someone could enlighten me.

I guess W1-2 = U1-U2 = K2 - K1 is only valid for isolated system, which should be a system without any external force involves except gravitational force.

I'm very confuse now, hope someone could help me.
 
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  • #2
w=f.d
f=m.g
d=distance moved
earth does -ve work , you do equal +ve.


ok!

+ve change in potiential energy always needs external energy source.

so W=U2-U1=m.g.d
 
  • #3
MechaMZ said:

Homework Statement


May i know how do i compute an energy conservative equation for the scenario below, which i don't understand.

If a book is lifted up by a force in order to make it moving upward with a constant velocity.
For conservation of total energy, W1-2 = U1-U2 = K2 - K1
If the object is moving in a constant velocity, isn't K2 - K1 = 0
However, U1 is not equal to U2.

It seems not correct obviously, hope someone could enlighten me.

The work done by non conservative forces (such as the lifting force on the book) is
[tex] W_{nc} = (U_2 - U_1) + (K_2 - K_1)[/tex] or in its alternate form, [tex]W_{nc} = \Delta U + \Delta K [/tex]

I guess W1-2 = U1-U2 = K2 - K1 is only valid for isolated system, which should be a system without any external force involves except gravitational force.

I'm very confuse now, hope someone could help me.
For a system subject to conservative forces only (like gravity or spring forces), then [tex] (U_2 - U_1) + (K_2 -K_1) = 0 [/tex], or [tex]\Delta U + \Delta K =0 [/tex], and the work done by such conservative forces is [tex] W_c = U_1- U_2[/tex], or [tex] W_c = - (\Delta U)[/tex] in its alternate form.

For a system subjct to both conservative and non conservative forces, then the total work done by those forces is [tex]W_T = (K_2- K_1)[/tex], or [tex]W_T= \Delta K[/tex]

staraet's answer for the work done by the lifting force is also correct.

This can get confusing for sure, but actually, I'm not exactly sure what your question is. Mechanical Energy (U + K) is NOT conserved when non-conservative forces that do work are acting.
 
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  • #4
PhanthomJay said:
For a system subjct to both conservative and non conservative forces, then the total work done by those forces is [tex]W_T = (K_2- K_1)[/tex], or [tex]W_T= \Delta K[/tex]

why we no need to include the [tex]\Delta U[/tex]? What if the object is in a falling motion with air resistive force acting on it.

Could i write it as: mg([tex]\Delta h[/tex]) - Ffriction([tex]\Delta h[/tex]) = [tex]\Delta K[/tex] + [tex]\Delta U[/tex]

or i should write it as without taking the work done by gravitational force: - Ffriction([tex]\Delta h[/tex]) = [tex]\Delta K[/tex] +[tex]\Delta U[/tex]
 
  • #5
always think in terms of gain and loss

we some thing goes along only acting force , it gains k.e
so decreases its p.e

when ball falls, so it means, going along a force, so increases k.e (say after dt);
then if u find k.e is constant-- it means body has spent that k.e in either heat, vibrational,mass or something in that dt time.
then write equations. don't write before....

here friction is heat. so E spent in heat= mgh
 
  • #6
I think my problem is I don't understand between work done, kinetic energy, and potential energy.
 
  • #7
I suggest sticking with PhanthomJay's first equation:
PhanthomJay said:
The work done by non conservative forces (such as the lifting force on the book) is
[tex] W_{nc} = (U_2 - U_1) + (K_2 - K_1)[/tex] or in its alternate form, [tex]W_{nc} = \Delta U + \Delta K [/tex].

As you realize for your example of lifting a book, K2=K1=0. Also, Wnc is the work W1-2 done by lifting, so in that case

W1-2 = U2 - U1

If instead we have an isolated system with only conservative forces such as gravity, we have Wnc = 0 and conservation of mechanical energy applies. PhanthomJay's equation then becomes:

0 = U2 - U1 + K2 - K1

this is often rewritten in the form

U1 + K1 = U2 + K2

and is simply a statement that the total energy (potential + kinetic) does not change.
 

1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is dependent on the mass and velocity of the object. The formula for kinetic energy is KE = 1/2 * m * v^2, where m is the mass and v is the velocity of the object.

2. How is kinetic energy different from potential energy?

Kinetic energy is the energy of motion, while potential energy is the energy an object possesses due to its position or configuration. An object has potential energy because of its potential to move or do work. For example, a stretched rubber band has potential energy because it has the potential to snap back to its original shape.

3. What factors affect the amount of potential energy an object has?

The amount of potential energy an object has depends on its position, height, and mass. The higher an object is, the more potential energy it has. Similarly, the heavier an object is, the more potential energy it has. The formula for potential energy is PE = m * g * h, where m is the mass, g is the acceleration due to gravity, and h is the height of the object.

4. How is energy conserved in a closed system?

In a closed system, energy can neither be created nor destroyed, but it can be transformed from one form to another. This means that the total amount of energy in a closed system remains constant. In the case of kinetic and potential energy, as an object falls, its potential energy decreases while its kinetic energy increases, but the total amount of energy remains the same.

5. How can we use the conservation of energy to our advantage?

The conservation of energy is a fundamental law of physics that allows us to predict and understand the behavior of systems. It also allows us to design and develop technologies that harness energy from various sources, such as wind, water, and sunlight. By understanding the principles of energy conservation, we can create more efficient and sustainable energy systems.

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