Momentum Notes

Momentum

• Momentum is the quantity of "motion."
• Objects with more momentum are harder to stop.
• Symbol: p
• Unit: kg m/s
• Vector (Direction is the same as velocity)
• Formula: $p = m v$
  • p is momentum
  • m is mass
  • v is velocity

Change in Momentum

• Impulse is a force exerted over time which causes a change in momentum.
• $F = m a$
• $F = m (∆v/t)$
• $F t = m ∆v$
• $F t = ∆p$
• An impulse (Force exerted over time) causes and is equal to change in momentum
• $\Delta p = p<em>f - p</em>i$
• $\Delta p = m (v<em>f - v</em>i)$
• $\Delta p = mv<em>f - mv</em>i$
• $\Delta p = m \Delta v$
• $\Delta p$ is directly proportional to mass and also to $\Delta v$
• $F = \frac{\Delta p}{t}$
• Force is directly proportional to $\Delta p$ and inversely proportional to impact time

Engineering Design Process

• Identify the problem
• Explore: Find out what others have done
• Design: Think up lots of ideas, pick one and make a plan
• Create: Use your plan to build your idea
• Try it out: Test your idea
• Make it better: Think about how your design could be improved

Conservation of Momentum

• System: A portion of the universe selected for study.
• Closed system: no objects enter or leave.
• Isolated system: no net force on the system from outside.
• Conservation: A quantity is "conserved" if the total amount stays the same within the system.
• Law of Conservation of Momentum: In a closed, isolated system, the total momentum stays the same.
• $p<em>{total} = p'</em>{total}$

Types of Collisions

• Elastic Collision: Objects bounce off each other. Momentum is conserved.
• Inelastic Collision: Objects stick together after the collision. Momentum is conserved.
• Recoil/Explosion: Objects start together and separate due to an internal force. Momentum is conserved.

Problem Solving Steps

1. Identify type of collision, the dividing event and draw before and after pic with arrows
2. Write and label knowns under the pics
3. Write the situation-specific equation, plug in.
4. Algebra (Start with Total Momentum!)

P-Conservation Notation

• Subscripts denote which object: $p<em>a v</em>2$
• An apostrophe is used to denote “later” $p’_a$