Unit 3.4 – Impulse

What is Impulse?

• $F$ = Force applied.
• $t$ = Time for which the force acts.
• $\mathrm{\Delta }p$ = Change in momentum ($p_{\text{final}}-p_{\text{initial}}$).
• Units: The SI unit of impulse is $\text{N.s}$ (Newton-seconds), which is equivalent to $\text{kg.m/s}$ (the unit of momentum).

Key Points About Impulse

1. Relation Between Impulse and Momentum:
   • Impulse causes a change in momentum.
   • A larger force or a longer duration of force results in a greater change in momentum.
2. Direction of Impulse:
   • Impulse is a vector quantity, and its direction is the same as the direction of the force applied.
3. Applications of Impulse:
   • Impulse helps us understand real-life phenomena like collisions, safety measures, and sports.

Real-Life Examples of Impulse

1. Catching a Ball:
   • When a cricket player catches a fast-moving ball, they lower their hands to increase the time of contact. This reduces the force exerted on their hands because:
   $$F\mathrm{.}t=\mathrm{\Delta }p$$
   By increasing $t$, the force $F$ decreases.
2. Car Crashes and Airbags:
   • During a car crash, airbags inflate to increase the time over which the passenger's momentum changes. This reduces the force experienced by the passengers, minimizing injuries.
3. Hitting a Nail with a Hammer:
   • A hammer delivers a large force over a very short time, creating a significant impulse that drives the nail into the wood.
4. Kicking a Football:
   • When a football is kicked, the force applied by the foot over a short time changes the ball's momentum, making it move forward.

Examples to Understand Impulse

Example 1:

• Solution:

Example 2:

• Solution:
  • Initial momentum ($p_{\text{initial}}$) = $0\text{kg.m/s}$ (since the car starts from rest).
  • Final momentum ($p_{\text{final}}$) = $m\mathrm{.}v=1000.20=20,000\text{kg.m/s}$.
  • Impulse ($J$) = $\mathrm{\Delta }p=p_{\text{final}}-p_{\text{initial}}=20,000-0=20,000\text{N.s}$.

Example 3:

• Solution:
  • Initial momentum ($p_{\text{initial}}$) = $m\mathrm{.}v=\mathrm{0.06.}(-30)=-1.8\text{kg.m/s}$ (negative sign indicates opposite direction).
  • Final momentum ($p_{\text{final}}$) = $m\mathrm{.}v=\mathrm{0.06.30}=1.8\text{kg.m/s}$.
  • Change in momentum ($\mathrm{\Delta }p$) = $p_{\text{final}}-p_{\text{initial}}=1.8-(-1.8)=3.6\text{kg.m/s}$.
  • Impulse ($J$) = $\mathrm{\Delta }p=3.6\text{N.s}$.
  • Average force ($F$) = $\frac{J}{t}=\frac{3.6}{0.02}=180\text{N}$.