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Momentum

Momentum. Review Energy, Intro Momentum Impulse-Momentum Examples of Impulse-Momentum Conservation of Momentum Inelastic, Elastic, and Indeterminate Collisions Indeterminate Collision Examples. Energy vs. Momentum. Energy

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Momentum

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  1. Momentum • Review Energy, Intro Momentum • Impulse-Momentum • Examples of Impulse-Momentum • Conservation of Momentum • Inelastic, Elastic, and Indeterminate Collisions • Indeterminate Collision Examples

  2. Energy vs. Momentum • Energy • Useful with conservative forces – where work only depends on difference of 2 endpoints. • Momentum • Useful in collisions – where objects exert equal and opposite forces by action-reaction.

  3. Vectors vs. Scalars • Chapter 2 – kinematics VECTOR • Chapter 3 – 2-D kinematics VECTOR • Chapter 4 – Newton’s Laws VECTOR • Chapter 5 – Circular Motion VECTOR • Chapter 6 - Energy SCALAR • Chapter 7 - Momentum VECTOR • (we only do in one dimension)

  4. Review of Work/Energy • Start with: • Along arbitrary path • Each term product of vectors, hence scalar • Multiply by ½m: • Scalar energy • Scalar work • Important Points • Work – force in direction of distance same as distance in direction of force • Multiple –sum of works same as work of sums, can neglect some works • PE – some works can be treated as change in PE

  5. Intro to Impulse/Momentum • Start with • vector expression • (back to x and y components) • Multiply by scalar m: • vector momentum • vector impulse • Notes • Momentum mv increased or decreased by addition of impulse Ft • Symbol p = mv, units kg-m/s • Momentum is vector, though we only do in one dimension. impulse momentum momentum

  6. Use of Momentum F12 = force on 1 due to 2 • Collisions 2 1

  7. Impulse/Momentum Example 1 • Tennis ball leaves racquet at speed 55 m/s. Mass is .06 kg and contact time 4 ms (4 x 10-3 s). Estimate force. • Change in momentum • Impulse

  8. Impulse/Momentum Example 2 • Water leaves hose at rate 1.5 kg/s with speed 20 m/s. Aimed directly at side of car which stops it. Estimate force of a) car on water, b) water on car. • Change in momentum each second • Impulse (note negative) • Force on water (note negative) • Force on car (note positive)

  9. Impulse/Momentum Example 3 A 0.145 kg baseball pitched at 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52 m/s. If the contact time between the bat and ball is 3 ms, calculate the average force on ball and bat during the hit. -39 m/s • Change in momentum • Impulse • Force on ball (note positive) • Force on bat (note negative) 52 m/s

  10. Conservation of Momentum F12 = force on 1 due to 2 • Collisions 2 1

  11. Conservation of Momentum • Too many variables – 3 possibilities • Inelastic – eliminate variable • Elastic - generate 2nd equation • Indeterminate - need more info

  12. Case 3 - Indeterminate • Conservation of momentum

  13. A little nuclear physics (Indeterminate) • Could convert “u” to kg, but conversion would just cancel in every term! • Conservation of momentum – original nucleus on left, products on right

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