Momentum and Impulse Study Notes

Momentum (p): The momentum of a moving object is calculated as the product of its mass ($m$) and its velocity ($v$).
- Formula: p = mv
- Units: kg·m/s
Impulse (I): The change in momentum of an object when a force ($F$) is applied over a period of time ($t$).
- Formula: I = Ft
- Relationship: Impulse equals the change in momentum.
Acceleration: The rate of change of velocity over time.
- Formula: a = \frac{\Delta v}{\Delta t}
Factors affecting momentum:
- Mass of the object
- Velocity of the object
When is impulse zero?: An object with constant momentum (no change in velocity) has zero impulse.
Application of concepts:
- In collisions, the greater the difference in velocity and mass, the greater the change in momentum and impulse.
- Practical examples include vehicle collisions, sports scenarios, and rocket launches.

Finding momentum:
- Example: A bumper car with mass $280 ext{ kg}$ moving at a speed of $3.2 ext{ m/s}$.
  - p = mv = 280 ext{ kg} \times 3.2 ext{ m/s} = 896 ext{ kg·m/s}
Impulse calculation:
- Example: Force exerted by a rocket is $4.8 ext{ N}$ for $1.63 ext{ s}$.
  - I = Ft = 4.8 ext{ N} \times 1.63 ext{ s} = 7.82 ext{ N·s}
Finding force:
- Example: Impulse of $15 ext{ N·s}$ over a contact time of $0.1 ext{ s}$.
  - F = \frac{I}{t} = \frac{15 ext{ N·s}}{0.1 ext{ s}} = 150 ext{ N}