# Impulse

• By integrating over time both sides of Newton’s second law $F=\frac{dp}{dt}$, we create the concept called impulse
• $\text{imp}=\int{Fdt}=\Delta p$

• If the force is constant, we have

$\displaystyle \text{imp}=F\Delta t=\Delta p$

• Alternatively, we can work with the average force <F>,

$\displaystyle \text{imp}=\left\langle F \right\rangle \Delta t=\Delta p$

• We can infer from the change in momentum of a body (over a period of time) the impulse acting on the body (over that period of time).

p| = (2)(3) – (2)(-3) = 12 kg m s-1

• In the above elastic collision, the wall exerted a leftward impulse of 12 N s on the ball, while the ball exerted a rightward impulse of 12 N s on the wall.
• Assuming the duration of impact to be 0.2 s, the average force acting on the ball during the impact would have been 12 ÷ 0.2 = 60 N.

p| = (2)(3) – 0 = 6 kg m s-1

• In comparison, in the above completely inelastic collision, the impulse between the wall and the ball is only 6 N s.
• Assuming the duration of impact to be 0.2 s, the average contact force would have been 6 ÷ 0.2 = 30 N.

Demonstrations