Question

Show that impulse is the change of momentum.

Answer 1

If a very large force acts on an object for a very short time, then the force is impulsive force or impulse. If a Force (F) acts on an object in a very short time (∆t), then from Newton’s second law dp = f.dt

Integrating `int_i^f dp = int_{t_1}^{t_2} f dt`

P_f – P_i = F[t₁ – t₂]

P_i – initial momentum of the object at time t₁

P_f – Final momentum of the object at time t₂

P_f – P_i = ∆P = > Change is momentum

(t₂ – t₁) = ∆t = > Time interval

The above equation can be written as

∴ ∆P = F ∆ t.

i.e. `int_{t_1}^{t_2} F dt = j` is called the impulse and t₁ it is equal to change in momentum of the object is ∆P = F ∆ t. When F is kept constant.