# Power and kinetic energy relationship to speed

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

The relationship between work done on a body and its kinetic energy is very Change in Kinetic energy = ( * Mass * Final velocity^2) - ( Mass * Initial. Relation between momentum and kinetic energy. particle and a heavy one have the same velocity, the heavy one has more kinetic energy. in general, so, since velocity is a vector, momentum is also a vector, pointing in the same direction as the velocity, . Finally, it is useful to have a unit for rate of working, also called “power”. . How are these changes related to each other?.

### Work, Energy and Power

If the force is in the opposite direction as the displacement, then the angle is degrees. If the force is up and the displacement is to the right, then the angle is 90 degrees.

This is summarized in the graphic below. Power Power is defined as the rate at which work is done upon an object. Like all rate quantities, power is a time-based quantity.

Power is related to how fast a job is done. Two identical jobs or tasks can be done at different rates - one slowly or and one rapidly. The work is the same in each case since they are identical jobs but the power is different. The equation for power shows the importance of time: Special attention should be taken so as not to confuse the unit Watt, abbreviated W, with the quantity work, also abbreviated by the letter W. Combining the equations for power and work can lead to a second equation for power.

A few of the problems in this set of problems will utilize this derived equation for power. Mechanical, Kinetic and Potential Energies There are two forms of mechanical energy - potential energy and kinetic energy.

Potential energy is the stored energy of position. In this set of problems, we will be most concerned with the stored energy due to the vertical position of an object within Earth's gravitational field.

Kinetic energy is defined as the energy possessed by an object due to its motion. An object must be moving to possess kinetic energy. The amount of kinetic energy KE possessed by a moving object is dependent upon mass and speed. The bicycle would be traveling slower at the bottom of the hill than without the generator because some of the energy has been diverted into electrical energy. Another possibility would be for the cyclist to apply the brakes, in which case the kinetic energy would be dissipated through friction as heat.

Like any physical quantity that is a function of velocity, the kinetic energy of an object depends on the relationship between the object and the observer's frame of reference. Thus, the kinetic energy of an object is not invariant. Spacecraft use chemical energy to launch and gain considerable kinetic energy to reach orbital velocity. In an entirely circular orbit, this kinetic energy remains constant because there is almost no friction in near-earth space.

### Kinetic energy - Wikipedia

However, it becomes apparent at re-entry when some of the kinetic energy is converted to heat. If the orbit is elliptical or hyperbolicthen throughout the orbit kinetic and potential energy are exchanged; kinetic energy is greatest and potential energy lowest at closest approach to the earth or other massive body, while potential energy is greatest and kinetic energy the lowest at maximum distance. Without loss or gain, however, the sum of the kinetic and potential energy remains constant.

Kinetic energy can be passed from one object to another. In the game of billiardsthe player imposes kinetic energy on the cue ball by striking it with the cue stick. If the cue ball collides with another ball, it slows down dramatically, and the ball it hit accelerates its speed as the kinetic energy is passed on to it.

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.

- Mechanics: Work, Energy and Power
- Momentum, Work and Energy
- What is kinetic energy?

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.

## Kinetic Energy

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.