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).

impulseA

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.

impulseB

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

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