If we lift and object up, the net work is clearly zero because the kinetic energy after the lift and before the lift are the same (0). However, the object still seems to gain gravitational potential energy. How did it gain that energy?
[Physics] Work and Gravitational Potential Energy
free-body-diagramnewtonian-gravitynewtonian-mechanicspotential energywork
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Here are a few points to keep in mind:
- Potential energy is always described as the potential energy of the system. For example, the gravitational potential energy of the Earth-Moon system, belongs to the system as a whole, not the Earth or the Moon individually. So for your example, if you are for instance throwing a brick upwards, it would be the potential of the brick-Earth system.
- The Work-Energy Theorem can be written (in terms of conservative, non-conservative and other, external forces) as:
$$W_{tot}=W_{cons}+W_{non-cons}+W_{ext}=\Delta K = K_{f}-K_{i}$$
But for a conservative force, the definition of the associated potential energy is
$$W_{cons} = -\Delta U = -(U_{f}-U_{i})$$
and so our previous equation becomes: \begin{align*} W_{tot}=W_{cons}+W_{non-cons}+W_{ext}&=\Delta K = K_{f}-K_{i}\\ -(U_{f}-U_{i})+W_{non-cons}+W_{ext}&=\Delta K = K_{f}-K_{i}\\ K_{i}+U_{i}+W_{non-cons}+W_{ext}&= K_{f}+U_{f} \end{align*} If there are no external forces or non-conservative forces, then: $$K_{i}+U_{i} = K_{f}+U_{f}$$ So we see that we can either use the concept of the work done by gravity, OR we can use the concept of gravitational potential energy. But we don't want to do both at the same time, as then we would count the influence of gravity twice.
The first thing you must do is define your system.
If the system is the book alone the the external forces on the book are the force that you exert on the book and the gravitational attraction on the book by the Earth.
If the book starts and finishes at rest then there is no change in the kinetic energy.
The work done by you on the book is positive as the direction of the force that you exert on the book is the same as the displacement of the book.
The work done by the gravitational force due to the Earth is negative because the gravitational force is in the opposite direction to the displacement of the book.
If the two external forces are equal in magnitude and opposite in direction then the net work done on the book is zero (equal to the change in kinetic energy).
Of course one could reason that the net external force on the book is zero so the net work done by external forces on the book is zero.
There is no mention of gravitational potential energy because it is the energy associated with the book and the Earth as a system.
So now let's consider this system of the book and the Earth.
The external force is now the force that you apply on the book.
The force that the Earth exerts on the book is an internal force and its Newton third law pair is the force that the book exerts on the Earth.
When you do positive work separating the book and the Earth that work increases the gravitational potential energy of the book-Earth system.
If you released the book the separation between the book and the Earth will decrease and the gravitational potential energy of the system will decrease.
The book (and the Earth) would then have kinetic energy.
Usually only the motion and kinetic energy of the book is considered because the mass of the Earth is so much greater than the book.
This results in the speed and kinetic energy of the Earth being very much smaller that that of the book.
Best Answer
The kinetic energy is 0 even after you did work on it, is because gravitational force did equal and opposite work on it I.e. negative work. But gravity is a conservative force. The negative work done by such forces gets stored as potential energy. It's a property of conservative forces.