# Formula for momentum using mass and velocity relationship

### How is force related to momentum?

This equation does not correctly describe the motion of This is distinct from v, which is the velocity of the object itself. In each of these examples, a mass unit is multiplied by a velocity unit to provide a momentum unit. This is consistent with the equation for momentum. Momentum, Work and Energy. Michael Fowler, U. Va. Physics. With this convention, two people of equal mass coming together from opposite directions at the same speed rate of change of momentum = mass x rate of change of velocity.

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. 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.

## Momentum Formula

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.

## How is force related to momentum?

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. In terms of an equation, the momentum of an object is equal to the mass of the object times the velocity of the object.

The equation illustrates that momentum is directly proportional to an object's mass and directly proportional to the object's velocity. The units for momentum would be mass units times velocity units. In each of these examples, a mass unit is multiplied by a velocity unit to provide a momentum unit.

This is consistent with the equation for momentum. Momentum as a Vector Quantity Momentum is a vector quantity. As discussed in an earlier unit, a vector quantity is a quantity that is fully described by both magnitude and direction. The direction of the momentum vector is the same as the direction of the velocity of the ball.

### Momentum and Collisions

In a previous unit, it was said that the direction of the velocity vector is the same as the direction that an object is moving. As a vector quantity, the momentum of an object is fully described by both magnitude and direction.

**Relation between velocity, mass,momentum**

The Momentum Equation as a Guide to Thinking From the definition of momentum, it becomes obvious that an object has a large momentum if both its mass and its velocity are large. Both variables are of equal importance in determining the momentum of an object. Consider a Mack truck and a roller skate moving down the street at the same speed. The considerably greater mass of the Mack truck gives it a considerably greater momentum. Yet if the Mack truck were at rest, then the momentum of the least massive roller skate would be the greatest.

The momentum of any object that is at rest is 0.