Lecture on Impulse and Momentum

Introduction

• Discussion on impulse and momentum.
• Focus starts with understanding momentum.

What is Momentum?

• Definition: Momentum (p) = Mass ( \times ) Velocity.
• Concept: Mass in motion; any moving object has momentum.

Examples:

• A moving train has high momentum due to large mass.
• A sports car has substantial momentum due to high velocity.
• An airplane at rest has no momentum.

Properties of Momentum

• Vector Quantity: Derived from scalar (mass) ( \times ) vector (velocity).
• Direction: Momentum direction is that of motion.
• Units: Kilogram ( \times ) meters/second.

Example Problem

• A 10 kg block moving at 5 m/s east has momentum:
  • Calculated as: ( 10 \times 5 = 50 ) kg ( \times ) m/s east.
• Movement direction impacts momentum sign:
  • Right (east) = Positive momentum.
  • Left (west) = Negative momentum.

What is Impulse?

• Definition: Impulse (I) = Force ( \times ) Time.
• Units: Newton ( \times ) seconds.

Impulse-Momentum Theorem

• Impulse is equal to the change in momentum.
• Formula: ( \text{Impulse} = \Delta p = F \times \Delta t ).
• Equivalent units: Newtons ( \times ) seconds = kg ( \times ) m/s.

Understanding Force

• Force is the rate of change of momentum: ( F = \frac{\Delta p}{\Delta t} ).
• Related to Newton's Second Law: ( F = m \times a ).

Example Problem

• Setup: 50 kg block on frictionless surface, 200 N force applied for 5 seconds.
• Initial Conditions: Velocity = 10 m/s east.

Calculations

• Impulse (Part A):
  • ( I = F \times t = 200 \times 5 = 1000 ) N ( \times ) s.
• Change in Momentum (Part B):
  • Positive due to force direction matching velocity.
  • ( \Delta p = 1000 ) kg ( \times ) m/s.

Momentum and Velocity (Part C & D)

• Final Momentum:
  • ( p_{final} = m \times v_{final} = 50 \times 30 = 1500 ) kg ( \times ) m/s.
• Final Velocity:
  • Calculated from ( \Delta p = m \times (v_{final} - v_{initial}) ).
  • Resulting ( v_{final} = 30 ) m/s.

Conclusion

• Summarized the relationship between impulse and momentum.
• Discussed the application of the impulse-momentum theorem in solving physics problems.
• Encouraged further exploration of related topics and subscription to content.