The impulse-theorem states that the change in momentum of an object is equal to the impulse exerted on it
Explanation:
The impulse-theorem states that the change in momentum of an object is equal to the impulse exerted on it.
Mathematically, we have:
- The impulse is defined as the product between the force exerted (F) and the duration of the collision ([tex]\Delta t[/tex]):
[tex]I=F \Delta t[/tex]
- The change in momentum is equal to the product between the mass of the object (m) and the change in velocity ([tex]\Delta v[/tex]):
[tex]\Delta p = m \Delta v[/tex]
So, the theorem can be written as
[tex]F\Delta t = m \Delta v[/tex]
This theorem can be proved by using Newton's second law. In fact, we know that
[tex]F=ma[/tex] (1)
where a is the acceleration of the object. However, we can re-write the acceleration as the rate of change of velocity:
[tex]a=\frac{\Delta v}{\Delta t}[/tex]
Therefore, (1) becomes:
[tex]F=m\frac{\Delta v}{\Delta t}[/tex]
And by re-arranging,
[tex]F\Delta t = m \Delta v[/tex]
Which is exactly the formula of the impulse theorem.
Learn more about impulse and momentum:
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