General Physics: Momentum and Impulse

Welcome to the lesson on momentum and impulse, part of a comprehensive University-level physics series. The focus today is on understanding momentum and impulse before moving on to collisions in the next lesson.

Introduction

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Key Concepts

Momentum

• Definition: Momentum (symbol: ( p )) is a vector quantity equal to mass times velocity.
  • Formula: ( p = m \times v )
  • It depends on both mass and velocity.
  • Doubling mass or velocity doubles momentum; doubling both quadruples momentum.
  • Direction of momentum is the same as velocity.
  • Can be one or two-dimensional (linear momentum).

Impulse

• Definition: Impulse is a vector equal to force times the duration of time it acts.
  • Formula: ( I = F \times \Delta t )
  • Impulse changes an object's momentum.
  • Related through the Impulse-Momentum Theorem: ( I = \Delta p )
  • Units: Kilogram meter per second (kg·m/s), same as momentum.

Impulse-Momentum Theorem

• Impulse equals the change in momentum: ( F \Delta t = \Delta p )
• Derivation from Newton's Second Law: ( F = m \times a )
  • Acceleration ( a = \Delta v / \Delta t )
  • Rearranging gives ( F \Delta t = m \Delta v )
  • Simplifies to ( I = \Delta (mv) )

Sample Problems

Problem 1 - Momentum Calculation

• A 1200 kg car traveling at 20 m/s.
  • Momentum: ( 1200 \times 20 = 24000 ) kg·m/s

Problem 2 - Impulse and Velocity Change

• Car hits a cow applying avg. force of 90,000 N over 0.20 s.
  • Impulse: ( F \Delta t = 90,000 \times 0.20 = 18,000 ) kg·m/s (in the opposite direction)
  • New Velocity: Solving ( -18,000 = 1200(v_f - 20) ) gives ( v_f = 5.0 ) m/s

Problem 3 - Change in Momentum

• Car hit by a truck, moving backwards at 10 m/s.
  • Change in Momentum: ( \Delta p = m(v_f - v_i) = 1200(-10 - 20) = -36,000 ) kg·m/s

Problem 4 - Impulse Duration

• Baseball hit off a tee, initial speed 0, final speed 40 m/s, force 10,000 N.
  • Time: ( \Delta t = \frac{0.1 \times 40}{10,000} = 4.0 \times 10^{-4} ) seconds (0.4 ms)

Conclusion

• Understanding the relationship between impulse and momentum is crucial for solving physics problems involving force and motion.
• Emphasis on signs and directional vectors in calculations.
• Encouragement to like and support if the lesson was helpful, and happy studying!