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Impulse
The time integral of force. The net external impulse acting on a system over a given time interval is equal to the system's change in momentum.
Although some everyday interactions like [gravity] and friction result in stable forces whose effects can easily be analyzed with dynamics, many interactions are not steady. Consider, for example, the difference between a push and a punch. When you push something, you consciously use your muscles to apply a steady force to the target object. For this reason, pushing a bowling ball or a bean bag feels much the same, apart from the fact that the bean bag will probably deform more in response to the force. When you punch something, however, you simply let your fist fly. The force felt by the target object and the reaction force exterted on your fist are the result of the impact of your moving fist with the object. This impact is essentially out of your control. The force exterted are not determined directly by your muscles (though the faster your fist is moving, the greater the force will tend to be), but rather it is principally determined by the properties of your hand and the target object. Because of this fact, there is a dramatic difference between the results of punching a bean bag versus punching a bowling ball.
Such impact or collision forces are extremely common in everyday life. Almost any sport will involve collisions. Household activities like hammering nails or kneading dough require collisions. Understanding collisions is also of great importance to car manufacturers.
Unfortunately, the forces during a collision are very difficult to characterize. They change extremely rapidly in time (the entire duration of a typical collision is measured in milliseconds), and they manner in which they change is stronly dependent on the material properties of the objects undergoing the collision. Because of these complications, it is rare to see a detailed force profile for a collision. Instead, collisions are usually described by an effect that is much more easily observed: the resulting change in the motion of the participants. The impulse delivered by a collision is one measure of this change.
One Definition of Impulse
Vector Change in Momentum
Suppose an object experiences a sudden interaction that results in a dramatic change in the object's momentum. One definition of the impulse provided by the interaction is to calculate the numerical value of the change in the object's momentum. In other words, the impulse J is:
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Note that because momentum is a vector, the change in momentum is also a vector. Thus, the impulse is by defintion a vector quantity. As with any vector quantity, it is important to remember that the calculation of impulse really involves three equations, one for each component:
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Initial-State Final-State Diagrams
The vector nature of momentum means that it very important when calculating the change to carefully set up a coordinate system.
Integral form of Newton's Second Law
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