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Equations of Linear Momentum and Impulse in Physics

Learn about linear momentum and impulse in physics, equations, examples, and conservation of momentum in different scenarios. Understand the difference between inertia and momentum.

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Equations of Linear Momentum and Impulse in Physics

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  1. Take out tables. On a separate sheet:Make a list of every equation we’ve not yet used in this class.

  2. Here is your choice: a. I toss a bullet at you. b. I shoot a bullet at you from a gun.Which is more dangerous to you?Why?

  3. Linear Momentum&Impulse

  4. Linear Momentum = mass in motion A measure of how hard it is to stop an object. It is like a quantity of motion. How is it different from inertia?

  5. Momentum (p) depends on: mass & velocity of object. p = mvm in kg v in m/s Units are … kg m no name. s

  6. Momentum is aVector Quantity Same direction as velocity All Energy KE too is a scalar

  7. Ex 1. A 2250 kg pickup truck has v = 25 m/s east. What is the truck’s momentum? p = mv = (2250 kg)(25 m/s) = 5.6 x 104kg m s

  8. Change in momentum - accloccurs any time an object changes velocity (speed or direction).

  9. Momentum Change &Newton’s 2nd Law • F = ma • F = m(Dv/Dt) • FDt =mDv m (vf - vi) for const mass. • FDt = Dp Impulse. • Dp = Change in momentum

  10. Stand up • Try to hit a home run. • Try to drive a golf ball really far.

  11. Equations of Momentum Change • J =FDt = Dp Impulse = change momentum. • pf – pi. • Dp = mvf – mvi • for velocity change with constant mass can factor out mass you can write, • m (vf - vi) or mDv.

  12. Force is required to change velocity or momentum of a body in motion.Force must be in contact for some time.

  13. Increased force & contact time on object give greatest impulseDp = mDv.

  14. Hit a homerun needs large impulse. The more contact time, the less force needed to give same impulse D p.

  15. Impulse (J) is the momentum change. It has the same units. kg m or Ns s It is like force but includes a contact time component!

  16. Ex 2. How long does it take an upward 100N force acting on a 50 kg rocket to increase its speed from 100 to 150 m/s?

  17. F = 100 NDv = 50 m/sm = 50 kg Ft = mDv t = mDv F 50 kg(50 m/s) 100 kg m/s2 = 25 s.

  18. Concept: A pitcher throws a fastball to a catcher. Who exerts a larger force on the ball? Explain.

  19. Concept: Explain, in terms of impulse and momentum, how airbags help avoid injury in a car crash.

  20. Examples of Impulse/Change in Momentum • Baseball batter swinging through ball. • Applying brakes of car over time to stop.

  21. Ex 3. How long does it take a 250 N force to increase to speed of a 100 kg rocket from 10 m/s to 200 m/s?

  22. Ft = mDv t = mDv FF = 250 Nm= 100 kgDv =190 m/st = 100kg(190m/s) 250 kg m/s2. = 76 s.

  23. Ex 4. The speed of a 1200 kg car increases from 5 to 29 m/s in 12 s. What force accelerated the car? 2400 - N

  24. Ex 5: A 0.4 kg ball is thrown against a wall with a velocity of 15 m/s. If it rebounds with a velocity of 12 m/s:a) what was its Dv?b) What was its Dp?

  25. Dv = vf – vi.-12 m/s – (15 m/s) = - 27 m/s. Dp = mDv = 0.4kg(27m/s) =10.8 kg m/s

  26. How many water balloons does it take to stop a bullet? 3:30 • http://www.unwindly.com/i/772-How-Many-Water-Balloons-Does-It-Take-To-Stop-A-Bullet

  27. Running with momentum. 15 min. • https://www.youtube.com/watch?v=jLIyDfkQcsk • Relaxing with impulse.13 minutes. • https://www.youtube.com/watch?v=0nOHLThv2mw

  28. Understanding Car Crashes 22 minstart 8:53 • Hewitt Momentum 4:20 • https://www.youtube.com/watch?v=2FwhjUuzUDg http://www.youtube.com/watch?v=yUpiV2I_IRI

  29. Hwk read text 208 – 211do pg 214 #1- 4 conceptsdo p 211 #1 - 4. Impulse prbs.Also worksheet “Impulse Momentum”

  30. Which are units of Impulse? Nm N/s Ns N/m A ball mass 0.10 kg is dropped from 12-m. Its momentum just as it strikes the ground is: 1.5 kgm/s 1.8 kgm/s 2.4 kgm/s 4.8 kgm/s

  31. A 0.060-kg tennis ball, initially moving at 12 m/s, is struck by a racquet causing it to move in the opposite direction at a speed of 18 m/s. What is the impulse exerted by the racquet on the ball? 0.36 kgm/s 0.72 kgm/s 1.1 kgm/s 1.8 kgm/s

  32. Graphs

  33. Constant force f - t graph:Dp /Impulse is area under curve FDt. Force N

  34. Non-Constant ForceForce vs. time graph. The area under the curve = impulse or Dp change in momentum. What is the impulse during the 9 seconds of contact? 225 Ns

  35. Consv Momentum Demos.

  36. Conservation of Momentum If no external force acts on a closed system, the total momentum remains unchanged even if objects interact.

  37. What is a system? Two or more objects that interact in motion. One may transfer part or all of its momentum to the other(s). Common examples: collisions, explosions.

  38. One Ball transfers all its momentum.

  39. The astronaut transfers part of his momentum to the second astronaut.

  40. Conservation of Momentum Calc’s • Total momentum before = total after interactions. • Collisions. • Explosions • Pushing apart.

  41. To Calculate: SPbefore = Spafterm1v1 + m2v2 = m1fv1f + m2fv2f v1 and v2 velocities for objects one and two. m1 andm2 masses of objects

  42. Recoil From Explosions

  43. Recoil illustrates conservation of momentum where initial and final momentum = 0.0 = p1 + p2.

  44. 1. Two spring loaded lab carts A and B, explode apart from rest. Cart A is twice the mass of cart B. The final velocity of cart A is 2 m/s. What is the final momentum of the system? • 0

  45. 2. The cannon is 100kg and the cannonball is 5 kg. If the ball leaves the cannon with a speed of 100 m/s, find the recoil velocity of the cannon. - 5 m/s = vcf

  46. Before Firing After Firingm1v1 + m2v2 = m1fv1f + m2fv2f0 = (100kg)vcf + (5kg)(100m/s) -500 kgm/s = (100 kg) vcf - 5 m/s = vcf recoil velocity of cannon

  47. 3. A 63-kg astronaut is in spacewalk when the tether breaks. The astronaut throws a 10-kg oxygen tank directly away from the spaceship at 12 m/s. Assuming the astronaut was initially at rest, what is his final speed after throwing the tank? • 1.9 m/s

  48. Hwk. Consv Momentum wksht

  49. Collisions • Sticky • Bouncy

  50. Stick em together problems Let’s say a 4 kg fish swimming at 5 m/s, eats a 1 kg fish. What is their final velocity?

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