# Work and energy - explanation of definition [duplicate]

I have a question about the definition of energy. the definition is "ability to do work". what does it mean? what is the ability that the definition talks about? what is the meaning of ability in energy? I understood the concept of work, and it would be great if someone could explain to me the concept and definition of energy.

## marked as duplicate by Aaron Stevens, John Rennie energy StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); May 8 at 7:46

• Energy is the ability to do work, this means that if something has x Energy then it can do x Work. – SR810 May 7 at 16:49
• Think you need to be careful. Not all of the energy something has is necessarily available to do work. – Bob D May 7 at 16:55
• Possible duplicate of Is energy the ability to do work? – Aaron Stevens May 8 at 3:33

My favourite example of using the definition: Why do we say that a body of mass m moving at speed u has kinetic energy of $$\tfrac12 m u^2$$ ? Imagine this: a cart of mass m moving at speed $$u$$ on level ground has a rope trailing from it. Someone grabs hold of the rope and exerts a constant retarding force -F on the cart, bringing it to rest in a distance s, while being pulled a distance s himself/herself. The cart's acceleration is $$-F/m.$$ So using $$v^2=u^2+2as,$$ we have $$0=u^2+2\frac{(-F)}{m}s.$$ So$$Fs=\tfrac12 m u^2.$$ But the cart exerts a force $$F$$ on the person via the rope, so does work $$Fs.$$ The cart's ability to do work was $$\tfrac 12 m u^2,$$ because that is the amount of work it could do!

• @Phillip, +1, I like your derivation of the connection between Work and Kinetic Energy! Initially, I didn't understand why you used $v^2=u^2+2as$, as I had forgotten that $v$ corresponds to the final velocity and $u$ corresponds to the initial velocity of the mass. I found a demonstration of the use of this equation here. You set $v=0$ because that was the final velocity. Substituting $- \frac{F}{m}$, showing that Work equals Kinetic Energy was an unexpected surprise! – Thomas Lee Abshier ND May 11 at 2:02
• Good! In fact one doesn't need to assume a constant force or straight line motion; more sophisticated derivations use vectors for displacement, velocity and force. They also use some elementary calculus. – Philip Wood May 11 at 7:10

Energy is like a reservoir, which has been loaded with some flow of force say filled like a pond with work. It could give back that reserved work, in analogy with the pond some or all of its water.

But how much of it you can actually tap into has to do with many factors.

Again in analogy to the pond, you have to be at a lower level and also have enough room for all the water or energy.

Earthquake releases much energy, but a cardboard box can hardly take any of it, while a massive high-rise takes a lot.

Huge water reservoir behind a dam has much potential energy but if you want to tap it into a turbine you need to let some of it waste as the flow kinetic energy through the turbine.

So energy is capable of doing some work, but it needs means to deliver that work.

Roughly speaking, work is the transfer of energy from one thing to another due to the application of a force through a distance in the direction of the force. In order for something to be able to transfer energy to something else, it must possess, at minimum, the amount of energy transferred for conservation of energy.

Thus something that possesses energy is capable of doing work.