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Conservation of Momentum

Conservation of Momentum. Review. Yeah! I already know this. p: momentum m: mass v: velocity p = m v p tot = p A0 + p B0 = p A1 + p B1 p tot = m tot v 2  only if A & B stick together. Example. Steps to Solve a Problem. Draw a BEFORE (State 0) picture

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Conservation of Momentum

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  1. Conservation of Momentum

  2. Review Yeah! I already know this. p: momentum m: mass v: velocity p = m v ptot = pA0 + pB0 = pA1 + pB1 ptot = mtotv2 only if A & B stick together

  3. Example

  4. Steps to Solve a Problem • Draw a BEFORE (State 0) picture • Draw an AFTER (State 1) picture • Label everything • Find missing pieces • Find the total momentum • Solve for what you don’t know

  5. Before (0) + - • Make sure you include: • Before (0) • Arrows • + & -

  6. After (1) + - • Make sure you include: • After (1) • Arrows • + & -

  7. Label Everything Before (0) After (1) - +

  8. Label Everything Before (0) After (1) A B A B - + Label each object A or B For every object include: m, v, p Use subscripts to label m, v, and p with A or B Use subscripts to label v, and p with 1 or 2

  9. Label Everything Before (0) After (1) A B A B - + m = v = p = m = v = p = m = v = p = m = v = p = Label each object A or B For every object include: m, v, p Use subscripts to label m, v, and p with A or B Use subscripts to label v, and p with 1 or 2

  10. Label Everything Before (0) After (1) A B A B - + mA = vA = pA = mB = vB = pB = mA = vA = pA = mB = vB = pB = Label each object A or B For every object include: m, v, p Use subscripts to label m, v, and p with A or B Use subscripts to label v, and p with 0 or 1

  11. Label Everything Before (0) After (1) A B A B - + mA = vA0 = pA0 = mB = vB0 = pB0 = mA = vA1 = pA1 = mB = vB1 = pB1 = Label each object A or B For every object include: m, v, p Use subscripts to label m, v, and p with A or B Use subscripts to label v, and p with 0 or 1

  12. Label Everything Before (0) After (1) A B A B - + mA = vA0 = pA0 = mB = vB0 = pB0 = mA = vA1 = pA1 = mB = vB1 = pB1 = Fill in all the numbers from the problem:

  13. Label Everything Before (0) After (1) A B A B - + mA = vA0 = pA0 = mB = vB0 = pB0 = mA = vA1 = pA1 = mB = vB1 = pB1 = Fill in all the numbers from the problem: A 3100 kg red roadster moving at 52 m/s has a head on collision with a 8300 kg green jeep moving at -34 m/s. The roadster bounces off with a velocity of -45 m/s. What is the final velocity of the jeep?

  14. Label Everything Before (0) After (1) A B A B - + mA = vA0 = pA0 = mB = vB0 = pB0 = mA = vA1 = pA1 = mB = vB1 = pB1 = Fill in all the numbers from the problem: A 3100 kg red roadster moving at 52 m/s has a head on collision with a 8300 kg green jeep moving at -34 m/s. The roadster bounces off with a velocity of -45 m/s. What is the final velocity of the jeep?

  15. Label Everything Before (0) After (1) A B A B - + mA = vA0 = pA0 = mB = vB0 = pB0 = mA = vA1 = pA1 = mB = vB1 = pB1 = Use units to help you figure it out (kg = m, m/s = v, kgm/s = p): A 3100 kg red roadster moving at 52 m/s has a head on collision with a 8300 kg green jeep moving at -34 m/s. The roadster bounces off with a velocity of -45 m/s. What is the final velocity of the jeep?

  16. Label Everything Before (0) After (1) A B A B - + mA = 3100 kg vA0 = 52 m/s pA0 = mB = 8300 kg vB0 = -34 m/s pB0 = mA = 3100 kg vA1 = -45 m/s pA1 = mB = 8300 kg vB1 = pB1 = Use units to help you figure it out (kg = m, m/s = v, kgm/s = p): A 3100 kg red roadster moving at 52 m/s has a head on collision with a 8300 kg green jeep moving at -34 m/s. The roadster bounces off with a velocity of -45 m/s. What is the final velocity of the jeep?

  17. Label Everything Before (0) After (1) A B A B - + mA = 3100 kg vA0 = 52 m/s pA0 = ? mB = 8300 kg vB0 = -34 m/s pB0 = ? mA = 3100 kg vA1 = -45 m/s pA1 = ? mB = 8300 kg vB1 = ? pB1 = ? Fill in what you don’t know with question marks: A 3100 kg red roadster moving at 52 m/s has a head on collision with a 8300 kg green jeep moving at -34 m/s. The roadster bounces off with a velocity of -45 m/s. What is the final velocity of the jeep?

  18. Find Missing Pieces Before (0) After (1) A B A B - + mA = 3100 kg vA0 = 52 m/s pA0 = ? mB = 8300 kg vB0 = -34 m/s pB0 = ? mA = 3100 kg vA1 = -45 m/s pA1 = ? mB = 8300 kg vB1 = ? pB1 = ? If you know 2 out of 3 (m, v, p) you can find what’s missing.

  19. Find Missing Pieces Before (0) After (1) A B A B - + mA = 3100 kg vA0 = 52 m/s pA0 = ? mB = 8300 kg vB0 = -34 m/s pB0 = ? mA = 3100 kg vA1 = -45 m/s pA2 = ? mB = 8300 kg vB1 = ? pB1 = ? If you know 2 out of 3 (m, v, p) you can find what’s missing.

  20. Find Missing Pieces Before (0) After (1) A B A B - + mA = 3100 kg vA0 = 52 m/s pA0 = 161200 mB = 8300 kg vB0 = -34 m/s pB0 = -282200 mA = 3100 kg vA1 = -45 m/s pA1 = -139500 mB = 8300 kg vB1 = ? pB1 = ? If you know 2 out of 3 (m, v, p) you can find what’s missing. Use: p = mv

  21. Find Total Momentum Before (0) After (1) A B A B - + mA = 3100 kg vA0 = 52 m/s pA0 =161200 mB = 8300 kg vB0 = -34 m/s pB0 =-282200 mA = 3100 kg vA1 = -45 m/s pA1 =-139500 mB = 8300 kg vB1 = ? pB1 = ? ptot = pA0 + pB0 & ptot = pA1 + pB1

  22. Find Total Momentum Before (0) After (1) A B A B - + mA = 3100 kg vA0 = 52 m/s pA0 =161200 mB = 8300 kg vB0 = -34 m/s pB0 =-282200 mA = 3100 kg vA1 = -45 m/s pA1 =-139500 mB = 8300 kg vB1 = ? pB1 = ? ptot = pA0 + pB0 & ptot = pA1 + pB1 Use what you know: ptot = 161200 -282200 = -121000

  23. Find the Missing Momentum Before (0) After (1) A B A B - + mA = 3100 kg vA0 = 52 m/s pA0 =161200 mB = 8300 kg vB0 = -34 m/s pB0 =-282200 mA = 3100 kg vA1 = -45 m/s pA1 =-139500 mB = 8300 kg vB1 = ? pB1 = ? Use what you know and a little algebra: ptot = pA0 + pB0 & ptot = pA1 + pB1 ptot = -121000

  24. Find the Missing Momentum Before (0) After (1) A B A B - + mA = 3100 kg vA0 = 52 m/s pA0 =161200 mB = 8300 kg vB0 = -34 m/s pB0 =-282200 mA = 3100 kg vA1 = -45 m/s pA1 =-139500 mB = 8300 kg vB1 = ? pB1 = ? Use what you know and a little algebra: ptot = pA1 + pB1

  25. Find the Missing Momentum Before (0) After (1) A B A B - + mA = 3100 kg vA0 = 52 m/s pA0 =161200 mB = 8300 kg vB0 = -34 m/s pB0 =-282200 mA = 3100 kg vA1 = -45 m/s pA1 =-139500 mB = 8300 kg vB1 = ? pB1 = ? Use what you know and a little algebra: ptot = pA1 + pB1 -pA1 -pA1

  26. Find the Missing Momentum Before (0) After (1) A B A B - + mA = 3100 kg vA0 = 52 m/s pA0 =161200 mB = 8300 kg vB0 = -34 m/s pB0 =-282200 mA = 3100 kg vA1 = -45 m/s pA1 =-139500 mB = 8300 kg vB1 = ? pB1 = ? Use what you know and a little algebra: ptot = pA1 + pB1 -pA1 -pA1 pB1 = ptot – pA1

  27. Find the Missing Momentum Before (0) After (1) A B A B - + mA = 3100 kg vA0 = 52 m/s pA0 =161200 mB = 8300 kg vB0 = -34 m/s pB0 =-282200 mA = 3100 kg vA1 = -45 m/s pA1 =-139500 mB = 8300 kg vB1 = ? pB1 = ? Use what you know and a little algebra: pB1 = ptot – pA1 = -121000 - (-139500) = 18500

  28. Solve for What You Don’t Know Before (0) After (1) A B A B - + mA = 3100 kg vA0 = 52 m/s pA0 =161200 mB = 8300 kg vB0 = -34 m/s pB0 =-282200 mA = 3100 kg vA1 = -45 m/s pA1 =-139500 mB = 8300 kg vB1 = ? pB1 = 18500 Use p = mv and a little algebra:

  29. Solve for What You Don’t Know Before (0) After (1) A B A B - + mA = 3100 kg vA0 = 52 m/s pA0 =161200 mB = 8300 kg vB0 = -34 m/s pB0 =-282200 mA = 3100 kg vA1 = -45 m/s pA1 =-139500 mB = 8300 kg vB1 = ? pB1 = 18500 Use p = mv and a little algebra: pB1 = mBvB1

  30. Solve for What You Don’t Know Before (0) After (1) A B A B - + mA = 3100 kg vA0 = 52 m/s pA0 =161200 mB = 8300 kg vB0 = -34 m/s pB0 =-282200 mA = 3100 kg vA1 = -45 m/s pA1 =-139500 mB = 8300 kg vB1 = ? pB1 = 18500 Use p = mv and a little algebra: pB1 = mBvB1 mB mB .

  31. Solve for What You Don’t Know Before (0) After (1) A B A B - + mA = 3100 kg vA0 = 52 m/s pA0 =161200 mB = 8300 kg vB0 = -34 m/s pB0 =-282200 mA = 3100 kg vA1 = -45 m/s pA1 =-139500 mB = 8300 kg vB1 = ? pB1 = 18500 pB1 = mBvB1 mB mB . vB1 = pB1 mB

  32. Solve for What You Don’t Know Before (0) After (1) A B A B - + mA = 3100 kg vA0 = 52 m/s pA0 =161200 mB = 8300 kg vB0 = -34 m/s pB0 =-282200 mA = 3100 kg vA1 = -45 m/s pA1 =-139500 mB = 8300 kg vB1 = ? pB1 = 18500 vB1 = pB1 = 18500 mB 8300 kg vB1 = 2.2 m/s

  33. Celebrate!You Did It! J. Gabrielse

  34. Classwork • p. 210: 11 & 12

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