# Force momentum relationship

### The Open Door Web Site : IB Physics : THE RELATION BETWEEN FORCE AND MOMENTUM

The first of these, momentum, was actually introduced by the French scientist . Since (as we have just shown) force = rate of change of momentum, it follows. Explain the relationship between momentum and force. State Newton's second law of motion in terms of momentum. Calculate momentum given mass and. A: Force is a measure of the change of momentum over time. It can be written as F = mass x change in velocity / time. In practical terms, the.

As you bring your car to a halt when approaching a stop sign or stoplight, the brakes serve to apply a force to the car for a given amount of time to change the car's momentum. An object with momentum can be stopped if a force is applied against it for a given amount of time. A force acting for a given amount of time will change an object's momentum. Put another way, an unbalanced force always accelerates an object - either speeding it up or slowing it down.

### Momentum and Impulse Connection

If the force acts opposite the object's motion, it slows the object down. If a force acts in the same direction as the object's motion, then the force speeds the object up. Either way, a force will change the velocity of an object. And if the velocity of the object is changed, then the momentum of the object is changed. Impulse These concepts are merely an outgrowth of Newton's second law as discussed in an earlier unit. To truly understand the equation, it is important to understand its meaning in words.

In words, it could be said that the force times the time equals the mass times the change in velocity. The physics of collisions are governed by the laws of momentum; and the first law that we discuss in this unit is expressed in the above equation.

## Momentum and Impulse Connection

The equation is known as the impulse-momentum change equation. The law can be expressed this way: In a collision, an object experiences a force for a specific amount of time that results in a change in momentum.

**Matric part 1 Physics, Force and Momentum - Physics Ch 3 Dynamics - 9th Class**

The result of the force acting for the given amount of time is that the object's mass either speeds up or slows down or changes direction. The impulse experienced by the object equals the change in momentum of the object. In a collision, objects experience an impulse; the impulse causes and is equal to the change in momentum. Consider a football halfback running down the football field and encountering a collision with a defensive back.

The collision would change the halfback's speed and thus his momentum. If the motion was represented by a ticker tape diagramit might appear as follows: She catches and holds it, and because of its impact begins to roll backwards.

What is found on doing this experiment carefully is that after the catch, she plus the ball roll backwards at just one-tenth the speed the ball was moving just before she caught it, so if the ball was thrown at 5 meters per second, she will roll backwards at one-half meter per second after the catch.

Momentum is traditionally labeled by the letter p, so his definition was: 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? 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.

## How is force related to 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.

### Momentum, Work and Energy

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. 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.

- Momentum, Work and Energy