Mathematical Derivation in The Case of An Object of Constant Mass
Impulse J produced from time t1 to t2 is defined to be
where F is the force applied from t1 to t2.
From Newton's second law, force is related to momentum p by
Therefore
where Δp is the change in momentum from time t1 to t2. This is often called the impulse-momentum theorem.
As a result, an impulse may also be regarded as the change in momentum of an object to which a force is applied. The impulse may be expressed in a simpler form when both the force and the mass are constant:
It is often the case that not just one but both of these two quantities vary.
In the technical sense, impulse is a physical quantity, not an event or force. The term "impulse" is also used to refer to a fast-acting force. This type of impulse is often idealized so that the change in momentum produced by the force happens with no change in time. This sort of change is a step change, and is not physically possible. This is a useful model for computing the effects of ideal collisions (such as in game physics engines).
Impulse has the same units (in the International System of Units, kg·m/s = N·s) and dimensions (M L T−1) as momentum.
Impulse can be calculated using the equation
where
- F is the constant total net force applied,
- t is the time interval over which the force is applied,
- m is the constant mass of the object,
- v1 is the final velocity of the object at the end of the time interval, and
- v0 is the initial velocity of the object when the time interval begins.
Read more about this topic: Impulse (physics)
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