# Momentum and kinetic energy relationship to speed

### Difference Between Momentum And Kinetic Energy

Relativity, Momentum, and Kinetic Energy. William Bertozzi (as So, his experiment allowed him to see how kinetic energy varied with speed. In the classical. in general, so, since velocity is a vector, momentum is also a vector, pointing in the same . Kinetic energy is created when a force does work accelerating a mass and increases its speed. How are these changes related to each other?. Relation between momentum and kinetic energy. particle and a heavy one have the same velocity, the heavy one has more kinetic energy.

### Relativity, Momentum, and Kinetic Energy

By dropping weights from different heights into a block of clay, Willem 's Gravesande determined that their penetration depth was proportional to the square of their impact speed. Early understandings of these ideas can be attributed to Gaspard-Gustave Corioliswho in published the paper titled Du Calcul de l'Effet des Machines outlining the mathematics of kinetic energy.

William Thomsonlater Lord Kelvin, is given the credit for coining the term "kinetic energy" c. These can be categorized in two main classes: Kinetic energy is the movement energy of an object. Kinetic energy can be transferred between objects and transformed into other kinds of energy. For example, a cyclist uses chemical energy provided by food to accelerate a bicycle to a chosen speed.

On a level surface, this speed can be maintained without further work, except to overcome air resistance and friction. The chemical energy has been converted into kinetic energy, the energy of motion, but the process is not completely efficient and produces heat within the cyclist.

### Kinetic energy and momentum, Cactus

The kinetic energy in the moving cyclist and the bicycle can be converted to other forms. For example, the cyclist could encounter a hill just high enough to coast up, so that the bicycle comes to a complete halt at the top.

The kinetic energy has now largely been converted to gravitational potential energy that can be released by freewheeling down the other side of the hill. 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.

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.

- Kinetic energy and momentum
- The Difference Between Momentum And Kinetic Energy
- 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.

## Momentum, Work and Energy

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.

## Relativity, Momentum, and Kinetic Energy

You can generalize this result to say that the ratio of kinetic energy of two objects having the same momentum is the inverse ratio of their masses. This principle readily applies to firearms. When a bullet leaves a gun it has the same momentum as the gun which recoilsdue to conservation of momentum.

But the bullet has much more kinetic energy than the gun. Looking at this more deeply you realize that much more of the gunpowder energy was transferred to the bullet than the gun, in the form of kinetic energy.

As an analogy to the gun and bullet consider the figure below showing two blocks with a spring held between them. This spring represents the gunpowder which stores the energy pushing the bullet and gun apart, represented by the smaller block and larger block, respectively. Initially, the spring is compressed between the blocks. The spring is then released and pushes the two blocks apart.

**Momentum vs Kinetic Energy**

In this system momentum is conserved, and as shown previously, the kinetic energy of the smaller block of mass M2 is larger than the kinetic energy of the larger and heavier block of mass M1.