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Understanding Momentum, Collisions, and Newton's Laws of Motion

This introductory physics lesson by Dr. Robert MacKay at Clark College covers key concepts in mechanics, focusing on momentum and collisions. It explores Newton's laws of motion, defining momentum and impulse, and introducing the principle of conservation of momentum. The lesson also discusses elastic and inelastic collisions, including real-world applications like explosions and recoil. Students will learn how to calculate momentum and analyze different collision scenarios, enhancing their understanding of motion and interaction in physical systems.

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Understanding Momentum, Collisions, and Newton's Laws of Motion

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  1. Momentum and Collisions Dr. Robert MacKay Clark College, Physics

  2. Introduction • Review Newtons laws of motion • Define Momentum • Define Impulse • Conservation of Momentum • Collisions • Explosions • Elastic Collisions

  3. Introduction • Newtons 3 laws of motion • 1. Law of inertia • 2. Net Force = mass x acceleration • ( F = M A ) • 3. Action Reaction

  4. Law of interia (1st Law) • Every object continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it. • acceleration = 0.0 unless the objected is acted on by an unbalanced force

  5. Newton’s 2nd Law • Net Force = Mass x Acceleration • F = M A

  6. Newton’s Law of Action Reaction (3rd Law) • You can not touch without being touched For every action force there is and equal and oppositely directed reaction force

  7. Newton’s Law of Action Reaction (3rd Law) Ball 1 Ball 2 F2,1 F1,2 F1,2 = - F2,1 For every action force there is and equal and oppositely directed reaction force

  8. Momentum , p • Momentum = mass x velocity • is a Vector • has units of kg m/s

  9. Momentum , p (a vector) • Momentum = mass x velocity • p = m v • p = ? 8.0 kg 6.0 m/s

  10. Momentum , p • Momentum = mass x velocity • p = m v • p = 160.0 kg m/s 8.0 kg V= ?

  11. Momentum , p • Momentum is a Vector • p = m v • p1 = ? p2 = ? V= +8.0 m/s m1= 7.5 kg m2= 10.0 kg V= -6.0 m/s

  12. Momentum , p • Momentum is a Vector • p = m v • p1 = +60 kg m/s p2 = - 60 kg m/s V= +8.0 m/s m1= 7.5 kg m2= 10.0 kg V= -6.0 m/s

  13. Momentum , p • Momentum is a Vector • p = m v • p1 = +60 kg m/s p2 = - 60 kg m/s • the system momentum is zero., V= +8.0 m/s m1= 7.5 kg m2= 10.0 kg V= -6.0 m/s

  14. Newton’s 2nd Law • Net Force = Mass x Acceleration • F = M a • F = M (∆V/∆t) • F ∆t = M ∆V • F ∆t = M (VF-V0) • F ∆t = M VF- M V0 • F ∆t = ∆p Impulse= F∆t • The Impulse = the change in momentum

  15. Newton’s 2nd Law • Net Force = Mass x Acceleration • F ∆t = ∆p Impulse= F ∆t • The Impulse = the change in momentum

  16. Newton’s Law of Action Reaction (3rd Law) Ball 1 Ball 2 F2,1 F1,2 F1,2 = - F2,1 For every action force there is and equal and oppositely directed reaction force

  17. Newton’s Law of Action Reaction (3rd Law) Ball 1 Ball 2 F2,1 F1,2 F1,2 = - F2,1 F1,2∆t = - F2,1 ∆t ∆p2 = - ∆p1

  18. Conservation of momentum Ball 1 Ball 2 F2,1 F1,2 If there are no external forces acting on a system (i.e. only internal action reaction pairs), then the system’s total momentum is conserved.

  19. “Explosions”2 objects initially at rest • A 30 kg boy is standing on a stationary 100 kg raft in the middle of a lake. He then runs and jumps off the raft with a speed of 8.0 m/s. With what speed does the raft recoil? V=8.0 m/s after V=? M=100.0 kg M=100.0 kg before

  20. “Explosions”2 objects initially at rest V=8.0 m/s • A 30 kg boy is standing on a stationary 100 kg raft in the middle of a lake. He then runs and jumps off the raft with a speed of 8.0 m/s. With what speed does the raft recoil? after V=? M=100.0 kg M=100.0 kg before p before = p after 0 = 30kg(8.0 m/s) - 100 kg V 100 kg V = 240 kg m/s V = 2.4 m/s

  21. Explosions If Vred=9.0 m/s Vblue=? 9.0 m/s

  22. Explosions If Vred=9.0 m/s Vblue=3.0 m/s 9.0 m/s 3.0 m/s

  23. “Stick together”2 objects have same speed after colliding • A 30 kg boy runs and jumps onto a stationary 100 kg raft with a speed of 8.0 m/s. How fast does he and the raft move immediately after the collision? V=8.0 m/s V=? M=100.0 kg M=100.0 kg before after

  24. “Stick together”2 objects have same speed after colliding • A 30 kg boy runs and jumps onto a stationary 100 kg raft with a speed of 8.0 m/s. How fast does he and the raft move immediately after the collision? V=8.0 m/s V=? M=100.0 kg M=100.0 kg before after p before = p after 30kg(8.0 m/s) = 130 kg V 240 kg m/s = 130 kg V V = 1.85 m/s

  25. “Stick together”2 objects have same speed after collidingThis is a perfectly inelastic collision • A 30 kg boy runs and jumps onto a stationary 100 kg raft with a speed of 8.0 m/s. How fast does he and the raft move immediately after the collision? V=8.0 m/s V=? M=100.0 kg M=100.0 kg before after

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