# Mechanics force momentum and impulse relationship

### What are momentum and impulse? (article) | Khan Academy

the impulse of force can be extracted and found to be equal to the change in momentum of an object provided the mass is constant. In physics, the quantity Force • time is known as impulse. And since the The equation is known as the impulse-momentum change equation. The law can be. is a quantity that describes the effect of a net force acting on an object (a kind of " moving The impulse-momentum theorem states that the change in momentum of an object equals the impulse applied to it. Related concepts of dynamics.

## Momentum Concepts

It is only the overall net impulse that matters for understanding the motion of an object following an impulse. Watch this video on area under rate function to learn more about how to use the area under a curve to evaluate the product of the quantities on the axes. The concept of impulse that is both external and internal to a system is also fundamental to understanding conservation of momentum.

Momentum in space Most people are familiar with seeing astronauts working in orbit. They appear to effortlessly push around freely floating objects.

**Collisions: Crash Course Physics #10**

Because astronauts and the objects they are working with are both in free-fallthey do not have to contend with the force of gravity. However, heavy moving objects still possess the same momentum that they do on earth, and it can be just as difficult to change this momentum. Suppose that an emergency occurs on a space station and an astronaut needs to manually move a free-floating 4, kg space capsule away from a docking area.

On earth, the astronaut knows she can hold a 50 kg weight above herself for 3 seconds. How quickly could she get the capsule moving? The interaction involves a force acting between the objects for some amount of time. This force and time constitutes an impulse and the impulse changes the momentum of each object.

Such a collision is governed by Newton's laws of motion; and as such, the laws of motion can be applied to the analysis of the collision or explosion situation.

So with confidence it can be stated that In a collision between object 1 and object 2, the force exerted on object 1 F1 is equal in magnitude and opposite in direction to the force exerted on object 2 F2. Now in any given interaction, the forces which are exerted upon an object act for the same amount of time. You can't contact another object and not be contacted yourself by that object. And the duration of time during which you contact the object is the same as the duration of time during which that object contacts you.

### Force, Momentum, and Impulse

Touch a wall for 2. Such a contact interaction is mutual; you touch the wall and the wall touches you. It's a two-way interaction - a mutual interaction; not a one-way interaction. Thus, it is simply logical to state that in a collision between object 1 and object 2, the time during which the force acts upon object 1 t1 is equal to the time during which the force acts upon object 2 t2.

Now we have two equations which relate the forces exerted upon individual objects involved in a collision and the times over which these forces occur. It is accepted mathematical logic to state the following: Objects encountering impulses in collisions will experience a momentum change.

The momentum change is equal to the impulse. Thus, if the impulse encountered by object 1 is equal in magnitude and opposite in direction to the impulse experienced by object 2, then the same can be said of the two objects' momentum changes. The amount of momentum gained by one object is equal to the amount of momentum lost by the other object.

The total amount of momentum possessed by the two objects does not change. Momentum is simply transferred from one object to the other object. Put another way, it could be said that when a collision occurs between two objects in an isolated system, the sum of the momentum of the two objects before the collision is equal to the sum of the momentum of the two objects after the collision.

If the system is indeed isolated from external forces, then the only forces contributing to the momentum change of the objects are the interaction forces between the objects. As such, the momentum lost by one object is gained by the other object and the total system momentum is conserved. And so the sum of the momentum of object 1 and the momentum of object 2 before the collision is equal to the sum of the momentum of object 1 and the momentum of object 2 after the collision.

### Momentum and Collisions

The following mathematical equation is often used to express the above principle. The symbols v1 and v2 in the above equation represent the velocities of objects 1 and 2 before the collision.

And the symbols v1' and v2' in the above equation represent the velocities of objects 1 and 2 after the collision. Note that a ' symbol is used to indicate after the collision. Direction Matters Momentum is a vector quantity; it is fully described by both a magnitude numerical value and a direction.

The direction of the momentum vector is always in the same direction as the velocity vector. Because momentum is a vector, the addition of two momentum vectors is conducted in the same manner by which any two vectors are added.

For situations in which the two vectors are in opposite directions, one vector is considered negative and the other positive. Successful solutions to many of the problems in this set of problems demands that attention be given to the vector nature of momentum.

Two-Dimensional Collision Problems A two-dimensional collision is a collision in which the two objects are not originally moving along the same line of motion. They could be initially moving at right angles to one another or at least at some angle other than 0 degrees and degrees relative to one another.

In such cases, vector principles must be combined with momentum conservation principles in order to analyze the collision. The underlying principle of such collisions is that both the "x" and the "y" momentum are conserved in the collision.

The analysis involves determining pre-collision momentum for both the x- and the y- directions. If inelastic, then the total amount of system momentum before the collision and after can be determined by using the Pythagorean theorem. Since the two colliding objects travel together in the same direction after the collision, the total momentum is simply the total mass of the objects multiplied by their velocity.