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Momentum

Momentum. Notes (HRW p196). Momentum. Definition The measure of how difficult it is to stop a moving object Mass in Action! Formula p = mass * velocity, or p = mv Units kg.m/s Momentum is a vector !. Example. Q: What is the momentum of a 1000 kg Civic traveling at 30 m/s?

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Momentum

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  1. Momentum Notes (HRW p196)

  2. Momentum • Definition • The measure of how difficult it is to stop a moving object • Mass in Action! • Formula • p = mass * velocity, or • p = mv • Units • kg.m/s • Momentum is a vector!

  3. Example • Q: What is the momentum of a 1000 kg Civic traveling at 30 m/s? • p = mass x velocity = m x v • p = 1000 x 30 = 30,000kg·m/s • Q: What is the momentum of a 100,000 kg locomotive traveling at 30 m/s? • P = mass x velocity • P = 100,000 x 30 = 3,000,000kg·m/s • Q: What is the momentum of a 40,000 ton (40,000,000 kg) oil tanker traveling at 5 m/s? • P = m * v = 40,000,000 * 5 • P = 200,000,000kg.m/s

  4. Definition The product of the force (F) acting on an object and the duration of the force (t) Formula Impulse = F * t Units Newtons.seconds (N.s) Examples Striking a golf/foot/base ball Seatbelts (how do they work?) Auto safety developments since 50’s Impulse

  5. Impulse Example • Example:  Wall exerts a force of 10,000 N on the van. The contact time is 0.01 s. What is the impulse? • Solve: Impulse = F * t = 10,000 * 0.01 • Impulse = 100 N-s

  6. Impulse and Momentum Change • According to Newton’s 2nd Law • The application of a net force on an object will result in the object accelerating (aka changing velocity) • F = ma = m(Δv/t) = m(vf – vo)/t, but • Ft= mvf – mvo = pf – po thus • Ft (or impulse) = change in momentum • Ft = Δmv = mΔv • F = mΔv/t • F = m(vf – v0)/t (Newton’s 2nd law in momentum terms)

  7. Impulse Example • A 1000 kg Civic is traveling at 30 m/s and accelerates to 40 m/s in 10 seconds. • What is the momentum of the car before accelerating? • po = m*v = 1000 * 30 = 30,000kg.m/s • What is the momentum of the car after accelerating for 10 seconds? • pf = m*v = 1000*40 = 40,000kg.m/s • What is the change in momentum? • Δp = pf – po = 40,000 – 30,000 = 10,000kg.m/s • What is the impulse? • J = Change in momentum = 10,000kg.m/s • What is the net force that causes the change? • F = change in momentum/time = 10,000/10 = 1,000 N F*t = change in momentum = mΔv

  8. Impulse Example • A 1000 kg Civic is traveling at 30 m/s and hits a lamp post. • What is the momentum of the car while moving? • po = m*v = 1000*30 = 30,000 kg·m/s • What is the momentum of the car after hitting the post? • pf = m*v = 1000*0 = 0 kg·m/s • What is the change in momentum? • Δp = pf – po = 0 – 30,000 = -30,000 kg·m/s

  9. Ex. Momentum Change = Impulse • Impulse = change in momentum (final – initial) • Impulse = 0 – mv • Ft = -mv (momentum is a vector!) • F = mv/t (force felt is the momentum/duration of the applied force)

  10. Impulses and Contact Time How does momentum of the vehicle relate to the impulse in the 2 scenarios below? Force is spread over a longer duration Force is spread over a shorter duration!

  11. Summary: Momentum - Impulse • Interrelated • Momentum • Impulse • Change in momentum Change in momentum F*t = m(vf – vo) IMPULSE Force * time F*t Momentum Δp = mvf - mvo

  12. Summary

  13. Practice • A stationary 0.12 kg hockey puck is hit with a force that lasts for 0.01 seconds and makes the puck move at 20 m/s. With what force was the puck hit? • Impulse = Change in momentum • Ft = mΔv = m(vf – vo) • F = mΔv/t • F = 0.12 (20 – 0)/0.01 = 240 N

  14. Practice • If a 5kg object experiences a 10 N force for 0.1 second, what is the change in momentum of the object? • Solve • Change in momentum = impulse • Impulse = F*t • Change in momentum = F*t = 10*0.1 = 1N-s

  15. Practice • A 50 kg driver of a sports car is traveling at 35 m/s when she hits a large deer. She strikes the air bag/seatbelt combination that brings her body to a stop in 0.5 seconds. • What average force does the bag/belt exert on her? • Solve: m=50, vo=35, vf=0, t=0.5, F=? • F = m*(vf-vo)/t • F = 50*(-35)/0.5 = -3500 N

  16. Practice (continued) • What if the driver in the previous example was not wearing a seatbelt and there were no airbags, and the windshield stopped her head in 0.002 s. • What is the average force on her head? • Solve • F = 50*-35/0.002 = -875,000 N!!!

  17. Conservation of Momentum Sum of the momenta of all elements before the event = Sum of the momenta of all elements after the event Momentum Before firing = p(rifle) + p(bullet) = 0Momentum After firing = p(rifle) + p(bullet) = 0After firing, the opposite momenta cancel – direction is important in vector arithmetic!

  18. Conservation of Momentum – Collisions (aka events) • 2 basic types of collisions for analysis • Elastic • Bodies collide and bounce apart – no energy loss • Bowling ball/pin • Pool • Inelastic • Bodies collide and stick together – some energy transformation into heat • Auto rear-ender • Picking up an object (combining) • Real world – a bit of both!

  19. Momentum TableBefore vs After Equate the total momentum (before) with the total momentum (after) to solve!

  20. Practice using table • A 1000 kg Honda @ 30 m/s collides (head-on glancing blow) with a 2000 kg Camry @ 20 m/s. If the Honda continues @ 20 m/s, • what is the speed of the Camry after the impact? • Solve: Honda, Camry, collision • Total momentum (before) = Total momentum (after) • phonda + pcamry = phonda + pcamry • 1000*30 + 2000*(-20) = 1000*20 + 2000*v • 30,000 – 40,000 = 20,000 + 2000v • v = -15 m/s (negative direction)

  21. Practice using table • A 200 kg astronaut leaves the Shuttle for a space walk and while stationary his tether breaks. To return to the craft he throws a 2 kg hammer @ 3m/s directly away from the shuttle. • What is his returning speed? • Solve: astronaut, hammer, throw • pastro + phammer (before) = pastro + phammer (after) • 200*0 + 2*0 = 200*v + 2*3 • v = -200/6 = -0.03 m/s

  22. Practice using table • A 500 kg bumper car @ 5 m/s runs into the back of a similar car @ 2 m/s. If the 2nd car bounces forward at 4 m/s, • what is the speed of the 1st car? • Solve: bumper car #1, #2, collision • (p1 + p2)before = (p1 + p2)after • 500*5 + 500*2 = 500*v + 500*4 • 2500 + 1000 = 500v + 2000 • v = 3 m/s

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