Work as Change in Kinetic Energy vs Change in PE

[Hereformore]

Net Work = Change in Kinetic Energy. What about potential energy?

Homework Statement

When we say net work = change in kinetic energy, does that mean that if the height of an object changes (and its initial and final velocity) do not change, then the work done also equals the potential energy?

Sometimes I see texts saying work = change in potential energy, but i thought it was change in kinetic energy. Do they mean change in potential energy = work done by the force(s) that change the height of the object and change in kinetic energy = NET Work done?

Homework Equations

U = mgh
KE = 1/2mv^2

Work = Change in KE OR Change in PE (?)

The Attempt at a Solution

What confuses me is that if i raise a book from a height of 0 m to 5m, then the potential energy definitely changes but the kinetic energy does not change (0m/s initially and 0 m/s final).

So Change in kinetic energy in this case cannot equal change in potential. So here work does NOT equal change in kinetic energy.

 

[ehild]

When you speak about work, you need to specify the force that does the work and the object the work is done on.
The work-energy theorem states that the change of the kinetic energy of a point mass (particle) is equal to the work of all the forces acting on it. If a vertical upward force F acts on a particle and it rises from h₁ to h₂ , the work of the applied force is W_a= F(h₂-h₁) and the work of gravity is W_g = -mg(h₂-h₁). The work of all the forces is equal to the change of the KE:

KE₂-KE₁=Wa+Wg=(F-mg)(h₂-h₁).

If the KE does not change, the net work is zero, so Wa+Wg=0, the applied force is negative of the force of gravity.

We define the potential with respect to a place where the PE is set equal to zero. If it is the ground, the PE of a body at a point A is the work done by the gravitational force while the body moves from A to the ground. It is PE(A)=mgh_A.

If the body moves from h₁ to h₂, the potential energy changes by ΔPE=PE(h₂)-PE(h₁)=mg(h₂-h₁). That is equal the negative of the work done by gravity: W_g=-ΔPE. You can write the Work-Energy theorem in the form
W_a-ΔPE=ΔKE, that is, W_a=ΔPE+ΔKE. The work of the applied force is equal to the change of the total mechanical energy. In case the KE does not change, the work done by the applied force is equal to the change of the potential energy.

ehild

 

[Simon Bridge]

I'd like to add slightly to what ehild has said, at the risk of being a bit confusing:

What confuses me is that if i raise a book from a height of 0 m to 5m, then the potential energy definitely changes but the kinetic energy does not change (0m/s initially and 0 m/s final).

... that action does involve a change in KE ... between 0m and 5m the book must have some non-zero velocity. It follows that you did some work in addition to that against gravity by accelerating and decelerating the book.

It is possible to lift a book through a height without changing KE, and doing work, though.
This requires the book to already be in motion at a constant speed...

 

[CWatters]

What Simon said. A human lifting a book is complicated by the fact that a human can't recover the ke during the deceleration phase. In many other systems that energy can be recovered. Humans are also inefficient and consume energy even when not doing work lifting books. Sometimes best not to use humans in examples because they are so non ideal machines.

 

[HalfLostAndSearching]

I would like to clarify the relationship between work, change in kinetic energy, and change in potential energy. Work is defined as the force applied to an object multiplied by the distance it is moved in the direction of the force. This work can result in a change in the object's kinetic energy, which is the energy it has due to its motion, or a change in its potential energy, which is the energy it has due to its position in a gravitational field.

In the example given, where a book is raised from a height of 0 m to 5 m, there is indeed a change in potential energy, as the book is now at a higher position in the gravitational field. However, there is no change in kinetic energy because the book's velocity remains constant at 0 m/s. In this case, the work done by the force (your hand) is equal to the change in potential energy of the book.

In general, the work done by a force on an object can result in a change in both kinetic and potential energy. The net work done, or the total work done by all forces on an object, is equal to the change in its kinetic energy. This is because the work done by the force(s) that change the object's kinetic energy is equal to the change in kinetic energy itself.

In summary, work can result in a change in both kinetic and potential energy, but the net work done is equal to the change in kinetic energy. The equation "work = change in potential energy" is only applicable in cases where there is no change in kinetic energy. I hope this clarifies the relationship between work and changes in energy for you.