# Energy and work

I don't quite understand the concept of energy and work.

We can define energy as the ability to do work. An object moving at constant speed has kinetic energy. Does the object have the ability to do work? There is no net force acting on it.

Something that has a constant velocity[1] has a definite amount of kinetic energy. It would do work if it would exert a net force on something. Let's make a nice and simple model with two objects.

Let's call the first one a baseball. The baseball is flying through the vacuum[2], going it's merry little way. There is no net force on the baseball, and it has a definite amount of kinetic energy.

We have a second object too. A catchers glove. The catchers glove is stationary. It has no kinetic energy.

Right now, nothing is happening, no forces, no work, just a flying ball. But due to an astronomical coincidence, right as we're looking at this situation, the ball is approaching the glove, and hits it! The moment the ball hits the glove, we are in a different situation. The ball is exerting a force on the glove, and the glove on the ball[3]. This means the ball is no longer flying at a constant speed; it's slowing down. the catchers glove starts to move too - it's gaining the amount of kinetic energy that the ball is losing. It is said that the ball is performing work and the amount of work it performs is the amount of energy transferred between the ball and the glove.

Note however, that the ball started to do work only when it started to exert a force, and thus a force started to work on the ball[3].

So yes, an object with a constant speed/no net force working on it has kinetic energy, which is equivalent to the ability to do work - if it would exert force on something else, in which case it would no longer be true there is no net force working on it. So when it's still flying along at a constant speed, it has the potential to do work. As soon as it starts doing that work, it's no longer flying along at a constant speed.

You could, of course, make things more complicated, and add in a third body that exerts force on the ball equal and opposite to the force the glove exerts on the ball. In that case, there would still be a net force of zero on the ball, and it would not accelerate or slow down, but would still do work on the glove. That changes nothing fundamentally however, and would be equivalent of the third object exerting the force directly on the glove, with the ball taken out of the equation completely. It adds nothing to the understanding of the original question.

[1] or something on which no net force is working - these two statements are equivalent!

[2] yes, we are playing baseball in a vacuum. We're awesome like that.

[3] remember Newtons third law. If something is exerting a force on something else, that other thing is exerting a force on the first thing, equal in size, opposite in direction.

• Dear downvoter, I would really benefit from knowing why the downvote so I can keep it in mind for future answers! – Martijn Nov 14 '14 at 10:36

Yes, an object traveling at constant velocity has the ability to do work. Imagine a rock that has been thrown towards a nail sticking out of a board. Since the rock will drive the nail into the wood on impact, an event that involves a force being exerted over a distance, the flying rock must have had the ability to do work because of its motion. This ability is called kinetic energy. After impact, the rock will be moving slower or will have stopped because its kinetic energy was changed into nail-driving work.

Energy describes the ability of an object to do work on other things. A force acting on that object would increase or decrease it's energy. When the object exerts a force on something else, that energy is used up.

I'd just like to clear something up, in simple terms:

• ENERGY is something A BODY HAS
• WORK is something A FORCE DOES

Your flying baseball has lots of kinetic energy. When it collides with a basketball, there will be a pair of forces of equal magnitude and opposite direction, one on the baseball, the other on the basketball. These forces will produce work while they last: if one makes $W$ work on the basketball, its counterpart will make $-W$ (negative $W$) work on the baseball.

Your question is too broad to be answered clearly -- that is, you don't have a specific question, you want a lecture on energy vs work --, but I'll try to make some points that may help you anyway.

First, energy is a property of objects, while work is one type of process that elicits transfer of energy between objects or conversion of energy from one kind to another in the same object. Another such process is heat transfer.

You must understand that there are many kinds of energy, of which some are, on a simplified manner:

• Kinetic: when a body has speed;
• (Gravitational) Potential: when a body is lifted above the ground (more generally, when a body is inside of a force field, be it gravitational, electric etc, or when it's configured in an elastic state, like a spring);
• Thermal: when a body is hot.

In classical settings, energy is never destroyed or created, but transferred or converted via processes such as the aforementioned ones. Work happens when a force acts on a body along a distance. Heat transfer happens when two bodies with different temperatures are put in contact, such that heat flows from the hotter to the colder.

It's very important to note that work ONLY EXISTS when the point where the force acts MOVES. Otherwise, no energy changes. Let's see some examples:

1. A body is dropped ten meteres above the ground. Its weight is the force that is pushing him down. As he falls, his gravitational potential energy turns into kinetic energy (i.e his height decreases while his speed increases). Work is done.
2. A body lays stationary on a table. There are two forces on the body: its weight, pushing him down, and the normal force from the table, pushing him up. Both cancel each other. No energy is changed (e.g its height remains the same, so does its speed). Note that no point moves. No work is done.
3. I squeeze a strong spring with my bare hands. My hands make forces on the spring, whose ends move inwards, leaving it compressed. Some chemical energy of mine (from food) becomes potential energy in the spring (which may be released when the spring is let go of). Work is done.
4. I put that compressed spring between two very rigid walls, one end of the spring touching each wall. The spring pushes the walls, which push back. Nothing moves. The spring remains compressed. It has the same energy it had before being put between the walls. No work is done.
5. I take the spring back and put it between two heavy boxes on a frictionless surface. As the spring extends, the boxes are pushed outwards. In the end, the spring is relaxed, while the boxes are gliding away, at constant speed. Note that the point of contact between spring and box travels as the box is pushed. Spring potential energy becomes boxes' kinetic energy. Work is done.

CONCLUSION:

1. Work and energy are not synonyms. Work is a change in energies elicited by a force that travels.
2. Force does not imply work. As examples #2 and #4 showed, the mere existence of a force does not mean that energy is changed (i.e work is done). As I said, the point where the force acts must move.

NOTE: some has been said about a so-called "paradox" where, upon a human pushing into a stationary wall, energy is changed (the human and perhaps the wall heat up) while no work is done; as the answerer in that question made clear, that happens because the human muscle fibers do work to produce the force, which is dissipated as heat, which heats up the human, which may heat up the wall. It is a somewhat more complex situation, which still perfectly obeys the fundamental principles outlined here. Another example would be revving up a motor on a stationary car. In the end, the fuel energy spent just heats up the environment, without net work being produced.

An object moving at constant speed has kinetic energy. Does the object have the ability to do work?

An example:

If the object is a hammer and it is moving towards a nail, it has the ability to do work.

Let me give you an alternate explanation.

Every system in the universe has something to do with energy. The energy has different forms, and these forms are interconvertible between each other.

Let's say that such a system has some mechanical energy which is prevented from being converted to any other form. Now, this mechanical energy can be stored in the system as either kinetic or potential energy.

Suppose you want to convert some potential energy to kinetic energy or some kinetic to potential. The process of converting mechanical energy from potential to kinetic or vice-versa is known as doing work, and the 'amount' of energy that has been transferred from one form to the other is known as work.

To do work however, you need a force. How much force do you need to transfer that much energy (work) ? If the system is an object, the force needed is ${W \over d}$, where $W$ is the work needed to be done and $d$ is the distance through which the force moves the object in the process. How did we derive this formula ? - purely by experiment.

Work can be done in many ways, however. You can do pressure-volume work, for example. Even then, in each case work will have dimensions of $Force\cdot Distance$.

The 'force' I have described above is a conservative force as it coverts one form of mechanical energy to another form of mechanical energy itself and not some other different form of energy like heat. If it does convert mechanical energy to a different form of energy like heat, it is called a non-conservative force. However, the formula for work done by both forces is same: $W=F\cdot d$.

Now to your question: Yes, it can do work, provided it has the ability to exert a force on another object to change the mechanical energy of that object. You must realise that it cannot do work on itself to change its own mechanical energy.

I hope I've given a simple and straightforward answer and hope it helps.

I don't quite understand the concept of energy and work.

We can define energy as the ability to do work. An object moving at constant speed has kinetic energy. Does the object have the ability to do work? There is no net force acting on it

Work is just a hyponim of energy: energy is the potentiality, work is the concrete, actual transfer of kinetic energy to another body. If no kinetic energy is transfered to the other body tou have done no work. You have read in the link fron wiki you quote in OP, that if there is no displacement there is no work done. I know it is rather difficult to accept this definition, but that's the way it is.

The sketch on the right of the picture solves the intricate puzzle: ball B has energy KE (= 8 J), it is kinetic energy as it makes B travel at 4 m/s, but we can call the same entity (KE) with another name, if we consider it in relation to other bodies, in relation to A the same KE (and its value8J) is the work A has done on B, and still the same entity (KE) is the ability of B to do work (8J) on C

To focus the conceptual problem think of money: if you have 100$in your pocket you have the potentiality, the power of buying (energy) when you actually buy a mobile/cell phone you spend that money (work) and convert it into a phone. Edit: just to use this analogy to explain the paradox hinted by André and in the link quoted below, if you waste your money you just lose it and you do not acquire any (goods) phone. If you use a 100$ note to light up your cigarette, for example, you have burned (calories pushing the wall) it to no avail and you haven't acquired anything.

You say that you have done work on an object when that objects changes its KE: when it increases it is called positive work and when KE decreases it is called negative work

If you want to understand the historical reasons that produced this peculiar definition you can find here all the details, and, following the quoted links there, you can learn more about wasted energy.

• @AndréNeves, you are doing confusion, André, if you push a wall and it doesn't budge you are increasing thermal energy of the wall but doing no work. To raise a weight you must accelerate it and do work. :) . – bobie Nov 10 '14 at 15:55
• @AndréNeves, No this is just the paradox you missed in the other answer: that you spend energy but do no work. Try to read carefullly all the related links there and you'll understand. Now please, this noise can confuse OP, consider deleting all these not useful comments. :) – bobie Nov 10 '14 at 16:11
• @AndréNeves, the point is that you are confusing OP: the concept is already difficult to digest and from what you say you yourself haven't understood it. You are not expanding the answer, you are contradicting it. Your comment is incorrect because you are affirming that increasing the thermal energy of a wall by pushing it means doing work. That is false, if there is no diplacement there is no work. – bobie Nov 11 '14 at 6:55
• @AndréNeves, this last comment is not comprehensible, off-topic and, most of all, it is not nice , as it regards the person and not the post, André, just write an answers and fully and clearly explain your views, that is the correct way, when you disagree in many aspects with an answer. :) – bobie Nov 11 '14 at 7:22
• @dmckee, synonyms are words that have similar meaning. That does not mean that you can substitute one with the other in all contexts. 'little' and 'small' are synonyms but you cannot exchange them in any context. For other synonyms the restrictions can be stricter. The difference is clearly explained in the text. I used a term that could be easily understood by OP, I have edited the post using the correct linguistic/technical term, with a link to help him understand – bobie Nov 11 '14 at 9:15

Forces are how one models interactions between two different objects. Let's consider only contact interactions for now (which excludes gravitational and electric & magnetic interactions). In these cases, one can associate a work with a given force over an interval if the dot product between the force and displacement is non-zero.

Therefore, an object traveling on its own, undergoing no other interactions, does not have a "work" associated with it. Yes, it has kinetic energy, but it doesn't have work because there is no force with which to calculate a work.

• There is not net force, so he can do work on an object if he makes a force on that object and is also also interacting with a third object with an exactly opposite force (so the net force on it is zero) – Wolphram jonny Nov 10 '14 at 5:08
• There can be displacement with zero net force. – BMS Nov 10 '14 at 16:33
• yes, that is what I am saying, but you can have net zero force if you interact with two different objects that apply forces in opposite directions to you. So even if the net force on you is zero, and you move at constant speed, you can still make force, actually, you are doing force on the two objects separately too (I know my English is not good, I hope you get what I am trying to say and add it to your answer, because it was part of the question).And I do not want to post an answer myself, yours is already almost complete. – Wolphram jonny Nov 10 '14 at 17:10

Energy is the ability to do Work

is a usual definition in textbooks and schools.

But work is not the ability of energy (if i can use such a term for a second). This is made more explicit in thermodynamics.

For mechanics and Newton's laws. Work is associated to a specific force acting on a body and only in the direction of that force (body moving in a direction perpendicular to that force does no work).

So for the example of a body moving with constant velocity, thus no force acting, no work is done.

However one can say that the body has kinetic energy but this energy is not available for work.