# Kinetic energy and work relationship building

### What is kinetic energy? (article) | Khan Academy

For instance, when a moving car is brought to rest, the work done by the frictional force on the tires is equal to the kinetic energy of the car, KE=1/2 mv2. The word “work” as used in physics has a narrower meaning than it does in . Kinetic energy is created when a force does work accelerating a mass and. Kinetic energy is a scalar. The units are the same as for work (i.e. Joules, J). Relation bewteen KE and W: The work done on an object by a net force equals the.

The amount of kinetic energy gained by the skateboarder is 2, joules. That means that the work done by the force on the skateboarder was positive 2, joules. It's positive because the force on the skateboarder gave the skateboarder 2, joules.

## Momentum, Work and Energy

If a force gives energy to an object, then the force is doing positive work on that object. And if a force takes away energy from an object, the force is doing negative work on that object. Now imagine that the skateboarder, who's moving with 10 meters per second, gets stopped because he crashes into a stack of bricks.

The stack of bricks does negative work on the skateboarder because it takes away energy from the skateboarder. To find the work done by the stack of bricks, we just need to figure out how much energy it took away from the skateboarder.

- Work as the transfer of energy

Since the skateboarder started with 2, joules of kinetic energy and ends with zero joules of kinetic energy, it means that the work done by the bricks on the skateboarder was negative 2, joules. It's negative because the bricks took away energy from the skateboarder.

Let's say we instead lift the bricks, which are kilograms, upwards a distance of four meters. To find the work that we've done on the bricks, we could use Fd cosine theta.

### Momentum, Work and Energy

But we don't have to. We could just figure out the amount of energy that we've given to the bricks. Consider lifting the box of books to a high shelf. If you lift the box at a steady speed, the force you are exerting is just balancing off gravity, the weight of the box, otherwise the box would be accelerating.

Putting these together, the definition of work is: To get a more quantitative idea of how much work is being done, we need to have some units to measure work.

This unit of force is called one newton as we discussed in an earlier lecture.

## What is kinetic energy?

Note that a one kilogram mass, when dropped, accelerates downwards at ten meters per second per second. This means that its weight, its gravitational attraction towards the earth, must be equal to ten newtons. From this we can figure out that a one newton force equals the weight of grams, just less than a quarter of a pound, a stick of butter. The downward acceleration of a freely falling object, ten meters per second per second, is often written g for short.

Now back to work. In other words approximately lifting a stick of butter three feet. This unit of work is called one joule, in honor of an English brewer. To get some feeling for rate of work, consider walking upstairs. A typical step is eight inches, or one-fifth of a meter, so you will gain altitude at, say, two-fifths of a meter per second. Your weight is, say put in your own weight here! A common English unit of power is the horsepower, which is watts.

Energy Energy is the ability to do work. For example, it takes work to drive a nail into a piece of wood—a force has to push the nail a certain distance, against the resistance of the wood.

A moving hammer, hitting the nail, can drive it in. A stationary hammer placed on the nail does nothing. Another way to drive the nail in, if you have a good aim, might be to simply drop the hammer onto the nail from some suitable height. By the time the hammer reaches the nail, it will have kinetic energy.

It has this energy, of course, because the force of gravity its weight accelerated it as it came down. Work had to be done in the first place to lift the hammer to the height from which it was dropped onto the nail.

In fact, the work done in the initial lifting, force x distance, is just the weight of the hammer multiplied by the distance it is raised, in joules. But this is exactly the same amount of work as gravity does on the hammer in speeding it up during its fall onto the nail. Therefore, while the hammer is at the top, waiting to be dropped, it can be thought of as storing the work that was done in lifting it, which is ready to be released at any time.

To give an example, suppose we have a hammer of mass 2 kg, and we lift it up through 5 meters. This joules is now stored ready for use, that is, it is potential energy. We say that the potential energy is transformed into kinetic energy, which is then spent driving in the nail.

We should emphasize that both energy and work are measured in the same units, joules. In the example above, doing work by lifting just adds energy to a body, so-called potential energy, equal to the amount of work done. From the above discussion, a mass of m kilograms has a weight of mg newtons. It follows that the work needed to raise it through a height h meters is force x distance, that is, weight x height, or mgh joules.

This is the potential energy. Historically, this was the way energy was stored to drive clocks.

Large weights were raised once a week and as they gradually fell, the released energy turned the wheels and, by a sequence of ingenious devices, kept the pendulum swinging. The problem was that this necessitated rather large clocks to get a sufficient vertical drop to store enough energy, so spring-driven clocks became more popular when they were developed.

A compressed spring is just another way of storing energy. It takes work to compress a spring, but apart from small frictional effects all that work is released as the spring uncoils or springs back. The stored energy in the compressed spring is often called elastic potential energy, as opposed to the gravitational potential energy of the raised weight. Kinetic energy is created when a force does work accelerating a mass and increases its speed.