# How to understand energy？and the relation with work?

1. Apr 11, 2015

### ittechbay

I am very confused about concepts of energy and work.

I try to understand this way:
there are many kinds of energy.
every force is related with one kind of energy,but there is special one,the kinetic energy relate with the "sum force"

2. Apr 11, 2015

### integ8me

Energy is never created or destroyed, it can be transferred in different forms.
In a system there are energies that enter into the system, energies that exit the system and energies that exist within the system. Kinetic energy exists within a system. It is defined as v^2/2. Work is an energy that crosses the boundaries of a system, it is external. Work has different forms such as mechanical, and electrical. For example when you plug a pump into the wall, it converts electrical work into mechanical work on a fluid to increase the pressure.

3. Apr 12, 2015

### Vatsal Sanjay

I will give this a try.
Energy is the ability to do work. There are several ways to transfer energy across the system's boundaries. Work is one of those ways. You may say that I have used work and energy to explain each-other, that is because work and energy are two inseparable quantities. You cannot talk about work without talking about work. However, here is another way of looking at work. $$W= ∫F.ds$$
This quantity is defined as work. As you can see that the terms on the right hand side of the above equation, force (F) and differential displacement (ds) are both vectors whereas work is scalar. One way of analysing a system would be by analysing the forces involved. Another (scalar) method would be by analysing different work interactions and change in energy of the system.
Now about the kinetic energy. See for a mechanical system with no temperature change, the net work done by all the forces comes out to be equal to the change in kinetic energy (defined as $\frac{mv^2}{2}$ ) of the system. Its like the F=ma equation; just that now you are dealing with the scalar quantities.

4. Apr 12, 2015

### Pring

Energy could be deduced from time-reverse symmetry.

5. Apr 12, 2015

### Staff: Mentor

Actually, it is the time-translation symmetry, not the time-reverse symmetry. Noether's theorem applies to differentiable symmetries, not discrete symmetries. But your idea is otherwise correct.

6. Apr 12, 2015

### Pring

7. Apr 13, 2015

### Philip Wood

I very much approve of this as an introductory definition. Together with a definition of the work done by a force, it leads directly, and without hand-waving, to correct equations for kinetic energy and for potential energy in electric and gravitational fields. Arguably it needs tweaking to accommodate zero point energy and internal energy, but I've never known of students grounded in energy as ability to do work to be confused by energy in quantum and thermodynamic contexts.

8. Apr 14, 2015

### Philip Wood

High school teachers in the 1950s and 1960s were rightly criticised for an overemphasis on classifying 'types' of energy, and especially for drilling students into 'kinetic energy is converted into gravitational potential energy' – that sort of thing. The criticism (strongly supported by Richard Feynman) is at least two-fold… (1) Energy is a conserved quantity which doesn't morph in any useful sense, but our method of calculating it does. (2) Energy is too subtle an idea for very young students to be 'taught'. They should instead be learning to get a feel for how wheels, springs etc behave.

It's worth noting that heat, work, and internal energy is a complete classification scheme when using the laws of thermodynamics. Kinetic and potential are terms in a different scheme of classification which can run alongside the thermodynamic, if required. Thus heat conducting through a solid may be regarded as a flow of kinetic and potential energy, whereas heat radiated from a hotter body to a cooler may be regarded as a flow of e-m radiation. Hope this isn't controversial.

9. Apr 14, 2015

### vanhees71

In classical mechanics, the energy-conservation law is very well suited to be taught to high-school students, at least in one-dimensional motion. Take the most simple case of the free fall close to Earth. The equation of motion reads
$$m \ddot{z}=-m g=\text{const}.$$
In this case the force can be easily written in terms of a derivative, i.e., there's a potential
$$V(x)=m g z$$
such that
$$F(x)=-m g=-V'(z).$$
Then you have
$$m \ddot{z}=-V'(z).$$
Multiplying with $\dot{z}$ gives
$$m \dot{z} \ddot {z} =\frac{\mathrm{d}}{\mathrm{d} t} \left (\frac{m}{2} \dot{z}^2 \right)=-\dot{z} V'(z)=-\frac{\mathrm{d}}{\mathrm{d} t} V(z).$$
Integrating both sides of the equation, leads already to the energy-conservation law, because with an appropriate integration constant, $E$ you get
$$\frac{m}{2} \dot{z}^2=E-V(z) \; \Rightarrow \; \frac{m}{2} \dot{z}^2 + V(z)=E=\text{const}.$$
This should be possible to argue in high school. At least this is how we were taught it about 25 years ago in a German highschool.