Question

How do you use the impulse-momentum theorem?

Answer 1

Hint: The theorem that represents the change of momentum of an object equal to the applied impulse on the object is known as the impulse-momentum theorem. Impulse-momentum theorem applied in real life where rebounding situations occur.

Complete step by step answer:
As we know, the impulse theorem states that the change in momentum of an object is equal to the impulse applied to the object. The equation can be written as : \[\Delta p = F.\Delta t\]
Here, change of momentum \[ = \Delta p\]and, the impulse applied is \[F.\Delta t\] hence, the impulse is represented as the product of applied force \[(F)\] and the very short duration of time when the force is applied \[(\Delta t)\]. Momentum is the product of mass \[(m)\]and the velocity in a very short duration of time\[(\Delta v)\]so, the equation of momentum can be written as \[m.\Delta v\].
Impulse momentum theorem derivation: As Newton’s Second Law of motion states that the rate of change of the momentum of a body or the system is directly proportional to the applied force of the body or the system.
From the law get the equation of force : \[F = m.a\] (acceleration of the body\[ = a\], the mass\[ = m\], and applied force\[ = F\])
Let’s initial velocity\[ = u\]and final velocity\[ = v\] under acceleration of the object and taken time for the change of velocity is \[\Delta t\]
\[\therefore F = \]\[ma = \]\[\dfrac{{m(v - u)}}{{\Delta t}}\]
     \[ = \dfrac{{(mv - mu)}}{{\Delta t}} = \] \[\dfrac{{change{\text{ }}in{\text{ }}momentum}}{{\Delta t}}\]
So, \[F = \dfrac{{\Delta p}}{{\Delta t}}\]
Again, we can write \[\Delta p = F.\Delta t\]
If we consider force is constant, the impulse of the object is
Impulse \[(J) = F.\Delta t\]
\[\therefore \]Impulse \[(J) = Change{\text{ }}in{\text{ }}momentum\]

Note: We use impulse-momentum in everyday life in some way as the use of Newton’s second law. It is used in vehicles that use rocket or jet engines due to its application for variable mass allowing momentum and impulse to be used. Its use in various sports like tennis, badminton, golf, etc. Impulse momentum theory helps us to calculate the new value of a force applied to the current value.