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Linear Momentum & Impulse

Here is your choice: a. I toss the 15-kg bowling ball to you. b. I shoot a 20-g bullet at you. Which is more dangerous to you? Why?. Linear Momentum & Impulse. Define Linear Momentum = product of mass x velocity. A measure of how hard it is to stop an object.

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Linear Momentum & Impulse

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  1. Here is your choice: a. I toss the 15-kg bowling ball to you. b. I shoot a 20-g bullet at you.Which is more dangerous to you?Why?

  2. Linear Momentum&Impulse

  3. Define Linear Momentum = product of mass x velocity A measure of how hard it is to stop an object. It is like a quantity of motion. How is it different from inertia?

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

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

  6. Change in momentumoccurs any time an object changes velocity (speed or direction).

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

  8. 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.

  9. Increased force & contact time on object give greatest Dp = mDv.

  10. The more time in contact, the less force needed to change p.

  11. Impulse (J) is the momentum change. It has the same units. kg m or Ns s The quantity FDt (or Ft) is called impulse (J).

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

  13. Non-Constant ForceForce vs. time graph. The area under the curve = impulse or Dp change in momentum.

  14. Probs

  15. State Newton 3 • If 2 objects interact, the force exerted by on object A by object B (Fa,b), is equal in magnitude but opposite in direction to the force exerted on object B by object A, (-Fb,a).

  16. A bird flies above the earth’s surface. Earth pulls down on the bird with a force of 5-N and so:

  17. Consv MomentumDerive it.

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

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

  20. 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.

  21. One Ball transfers all its momentum.

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

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

  24. 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?

  25. Bg fish sm.fish Bg fish sm.fish m1v1 + m2v2 = m1fv1f + m2fv2f (4kg)(5m/s)+(1 kg)0 =(4kg)v1+(1kg)v2 But the final velocities are equal so factor out the vf: 20 kg m/s = vf (4+1kg) vf = (20 kg m/s) / (5kg) = 4m/s

  26. Find the final velocity of the cart and brick together A 2 kg brick is dropped on a 3 kg cart moving at 5.0 m/s.

  27. cart brick cart brickm1v1 + m2v2 = m1fv1f + m2fv2f(3kg)(5.0m/s) + 0 = (3kg)v1 + (2kg)v2150 kg m/s = v (3kg + 2 kg) (150 kg m/s )/5 kg = 3.0 m/s

  28. Elastic & Inelastic Collisions Totally Elastic: no KE lost at all (to heat, light, sound etc.) Usu. Involves objects that don’t make contact. Totally Inelastic: involves greatest loss of KE. Usu damage done. Most extreme case – objects stick together.

  29. Which is totally elastic? Inelastic?

  30. Inelastic Collisionmc = 1000 kg mt = 3000 kgvc = 20 m/s vt = 0pc = pt =

  31. m1v1 + m2v2 = m1fv1f + m2fv2f (1000kg)(20m/s) + 0 = (1000)v + (3000)v (20000 kg m/s) = (1000kg + 3000kg)v (20000 kg m/s) = (4000 kg)v (20000 kg m/s) = v4000 kg v = 5 m/s

  32. Elastic Collision mc = 1000 kg mt = 3000 kgvc = 20 m/s vt = 0 Find final velocity of the car if truck has final velocity of 10 m/s.

  33. m1v1 + m2v2 = m1fv1f + m2fv2f(1000kg)(20m/s) + 0 = (1000kg)vc+(3000kg)(10m/s) 20,000 kg m/s = (1000kg)vc+30000 kg m/s 20,000 kg m/s – 30,000 kg m/s = vc (1000kg) - 10 m/s = vc

  34. Recoil From Explosions

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

  36. 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.

  37. 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

  38. Ex: On July 4th my family likes to shoot off fireworks. One rocket was shot straight up, climbed to a height 18-m and exploded into hundreds of pieces in all directions at its highest point.Thinking about conservation laws, think about the rocket at its highest point just before & just after it explodes:How does the rocket’s momentum compare before & after the explosion?How does its KE compare before & after the explosion?

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