# Define momentum in terms of mass and velocity relationship

### Momentum, Work and Energy

Momentum relates both mass and velocity as a person has more momentum through an increase in mass or Originally Answered: What is the relation between speed and velocity? . Then take LCM of terms in the bracket and solve , we get. Momentum is traditionally labeled by the letter p, so his definition was: In other words, if something moving to the right was taken to have positive momentum, then one rate of change of momentum = mass x rate of change of velocity. Newton's second law of motion defines force as the product of mass times ACCELERATION (vs. velocity). Since acceleration is the change in velocity divided by.

After the catch, there is a total mass of 50kg moving at a speed of 0.

We have just invented these figures, of course, but they reflect what is observed experimentally. What about two people on rollerskates, of equal weight, coming directly towards each other at equal but opposite velocities—and when they meet they put their hands together and come to a complete halt?

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- Momentum - How it works
- How is force related to momentum?

In other words, if something moving to the right was taken to have positive momentum, then one should consider something moving to the left to have negative momentum. With this convention, two people of equal mass coming together from opposite directions at the same speed would have total momentum zero, so if they came to a complete halt after meeting, as described above, the total momentum before the collision would be the same as the total after—that is, zero—and momentum would be conserved.

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.

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.

## Momentum, Work and Energy

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.

## Momentum - Higher - AQA

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.

As a vector quantity, the momentum of an object is fully described by both magnitude and direction. 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. Objects at rest do not have momentum - they do not have any " mass in motion. The momentum equation can help us to think about how a change in one of the two variables might affect the momentum of an object.

The total mass of loaded cart is 1. If the cart was instead loaded with three 0. A doubling of the mass results in a doubling of the momentum. Similarly, if the 2.

### How it works - Momentum - Momentum and Inertia, Mass and Weight, Velocity and Speed

A quadrupling in velocity results in a quadrupling of the momentum. Click the button to view the answers. Determine the momentum of a