# Energy related to mass and velocity relationship

### Momentum, Work and Energy

There are many forms of kinetic energy - vibrational (the energy due to vibrational upon two variables: the mass (m) of the object and the speed (v) of the object. The following equation is used to represent the kinetic energy (KE) of an object. In physics, the kinetic energy of an object is the energy that it possesses due to its motion. . In SI units, mass is measured in kilograms, speed in metres per second, and the resulting kinetic energy is in joules. For example, one to double the speed. The kinetic energy of an object is related to its momentum by the equation. Distance, Velocity, Momentum, Force, Pressure, Work and Energy. Distance momentum: p = mv, where m is the mass in kg, and p is in kg m/s angular force due to gravity at the surface of the earth: Fg = mg downward, where g = m/s2 is.

Of course, in the discussion above we are restricting ourselves to motions along a single line.

It should be apparent that to get a definition of momentum that is conserved in collisions what Huygens really did was to tell Descartes he should replace speed by velocity in his definition of momentum. It turns out experimentally that in any collision between two objects where no interaction with third objects, such as surfaces, interferesthe total momentum before the collision is the same as the total momentum after the collision.

Now, the momentum is mv, mass x velocity. This means for an object having constant mass which is almost always the case, of course!

Now think of a collision, or any kind of interaction, between two objects A and B, say. In other words, since these are vectors, they are of equal length but pointing in opposite directions. This means that for every bit of momentum A gains, B gains the negative of that.

In other words, B loses momentum at exactly the rate A gains momentum so their total momentum remains the same. But this is true throughout the interaction process, from beginning to end.

**Mass? Energy? What's The Difference?!**

Therefore, the total momentum at the end must be what it was at the beginning. You may be thinking at this point: Nevertheless, we do know that momentum will be conserved anyway, so if, for example, the two objects stick together, and no bits fly off, we can find their final velocity just from momentum conservation, without knowing any details of the collision.

First, it only refers to physical work, of course, and second, something has to be accomplished. 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. 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.

### Kinetic and Potential Energy

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. 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.

Since the bicycle lost some of its energy to friction, it never regains all of its speed without additional pedaling. The energy is not destroyed; it has only been converted to another form by friction. Alternatively, the cyclist could connect a dynamo to one of the wheels and generate some electrical energy on the descent. 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.

### Physics for Kids: Kinetic Energy

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.

However, it becomes apparent at re-entry when some of the kinetic energy is converted to heat. Velocity, however, has nothing to do with an object's potential energy. The green ball has potential energy due to its height.

The purple ball has kinetic energy due to its velocity.

## Kinetic energy

Example Using A Roller Coaster One way to think of potential and kinetic energy is to picture a car on a roller coaster. As the car travels up the coaster it is gaining potential energy. It has the most potential energy at the top of the coaster. As the car travels down the coaster, it gains speed and kinetic energy. At the same time it is gaining kinetic energy, it is losing potential energy.

At the bottom of the coaster the car has the most speed and the most kinetic energy, but also the least potential energy. A car and a bicycle are traveling at the same speed, which has the most kinetic energy?