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Motion II

Motion II. Momentum and Energy. Momentum. Obviously there is a big difference between a truck moving 6 0 mi/ hr and a baseball moving 6 0 mi/hr. We want a way to quantify this. Newton called it Quantity of Motion. We call it Momentum. Definition: Momentum = (mass)x(velocity) p = m v

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Motion II

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  1. Motion II Momentum and Energy

  2. Momentum • Obviously there is a big difference between a truck moving 60 mi/hr and a baseball moving 60 mi/hr. • We want a way to quantify this. • Newton called it Quantity of Motion. We call it Momentum.

  3. Definition: Momentum = (mass)x(velocity) p = mv • Momentum is a vector. • Combination of mass and velocity • Large momentum for massive objects moving slowly or small objects moving quickly

  4. Newton’s 2nd Law • Note: Sometimes we write t instead of just t. They both represent the time interval for whatever change occurs in the numerator.

  5. Newton’s 2nd Law • Since p = mv, we have p = (mv) • If m is constant (not true for rockets and ballons), p = mv and v/t = a

  6. Rearrange Newton’s 2nd Law • This is the impulse • Impulse is the total change in momentum

  7. Example • Baseball • p = pf – pi = mvf– mvi F = p/t t is the time the bat is in contact with the ball v: bring the ball to rest, accelerate in other direction

  8. Ion Propulsion Engine: very weak force (0.1 N, about the weight of a paper clip) but for very long times (months) • Large momentum change • Very efficient

  9. A 70 kg person traveling at +15 m/s stops.What is the impulse? • 525 kgm/s • 1050 kgm/s • -525 kgm/s • -1050 kgm/s • 2100 kgm/s • -2100 kgm/s

  10. Example • 70 kg person traveling at 15 m/s stops. • Dp = pf – pi = 0 kgm/s – 1050 kg·m/s = -1050 kg·m/s • If the person is stopped by the windshield Dt = 0.01 s • What is the force involved?

  11. Force to stop 70 kg in 0.01s • -1050 N • -10500 N • -105000 N • -1050000 N

  12. Example • 70 kg person traveling at 15 m/s stops. • Dp = pf – pi = 0 kgm/s – 1050 kg·m/s = -1050 kg·m/s • If the person is stopped by an airbag Dt = 0.40 s • What is the force involved?

  13. Force to stop 70 kg in 0.40s • -1050 N • -2625 N • -5250 N • -105000 N

  14. Is the impulse the same in both cases? • Yes • No

  15. Crumple zones on cars increase the time for a car to stop. This greatly reduces the average force during accident. • Air bags do the same thing

  16. Conservation of Momentum • Momentum is always conserved within a system • “Momentum is conserved in all collisions.” • Momentum of a single object can be changed

  17. Conservation of Momentum • Newton’s 3rd Law requires F1 = -F2 • p1/t = -p2/t • Or • p1/t + p2/t = 0 • Or • p1 + p2 = 0 • NO NET CHANGE IN MOMENTUM

  18. Example: Cannon • 1000 kg cannon • 5 kg cannon ball Before it fires Pc + Pb = 0 Ptotal must be zero after it fires. If Vb= 400 m/s McVc + MbVb = 0 Vc = -MbVb/Mc = -(5kg)(400m/s)/(1000kg) = -2m/s

  19. ENERGY & WORK • In the cannon example, both the cannon and the cannon ball have the same momentum (equal but opposite). • Question: Why does a cannon ball do so much more damage than the cannon?

  20. ENERGY & WORK • In the cannon example, both the cannon and the cannon ball have the same momentum (equal but opposite). • Question: Why does a cannon ball do so much more damage than the cannon? • Answer: ENERGY

  21. ENERGY & WORK • Essentially, energy is the ability to make something move. • What transfers or puts energy into objects? • A push

  22. WORK • We will begin by considering the “Physics” definition of work. • Work = Force x displacement in direction of force • W=Fd • 1) if object does not move, NO WORK is done. • 2) if direction of motion is perpendicular to force, NO WORK is done

  23. Example • Push a block for 5 m using a 10 N force. • Work = (10 N) x (5 m) = 50 Nm = 50 kgm2/s2 = 50 J (Joules)

  24. I have not done any work if I push against a wall all day long without moving it. • True • False

  25. Doing WORK on a body changes its ENERGY • ENERGY is the capacity to do work. • The release of energy does work, and doing work on something increases its energy • Two basics type of energy: Kinetic and Potential.

  26. Kinetic energy: Energy of motion • Potential energy: Energy of situation • Position • Chemical structure • Electrical charge

  27. Kinetic Energy: Energy of Motion • Push a ball of mass m with a constant force. KE = W = Fd = (ma)d KE = (ma)(½ at2) = ½ m(at)2 =½ mv2 KE =½ mv2

  28. If the speed of the truck doubles what happens to its kinetic energy? • Increases by ½ • Doubles • Quadruples

  29. A 6000 kg truck travels at 10 m/s. What is its momentum? • 3000 kg∙m/s • 6000 kg∙m/s • 30000 kg∙m/s • 60000 kg∙m/s • 300000 kg∙m/s • 600000 kg∙m/s

  30. Potential Energy • Lift an object through a height, h. PE = W = Fd= (mg)h PE = mgh Note: We need to decide where to set h=0.

  31. Other types of energy • Electrical • Chemical • Thermal • Nuclear

  32. Conservation of Energy • We may convert energy from one type to another, but we can never destroy it. • Examples using only PE and KE (Mechanical Energy). KE + PE = const. OR KEi + PEi = KEf + PEf

  33. Conservation of Energy • Amount of mechanical energy (combined KE & PE) stays the same only if there is no friction

  34. Drop a rock off a 100m cliff • Call bottom of cliff h = 0 • Initial KE = 0; Initial PE = mgh • Final PE = 0 • Use conservation of energy to find final velocity mgh = ½mv2 v2 = 2gh

  35. 5 kg rock at top of 100 mcliff. What is its potential energy? • 4900 J • 9800 J • 500 J • 980 J

  36. For our 100 m high cliff • Note that this is the same as we got from using kinematics with constant acceleration

  37. 5 kg rock falls from a 100 mcliff. What is its kinetic energy at bottom? • 500 J • 2450 J • 4900 J • 9800 J

  38. A 5 kg ball is dropped from rest from the top of a 300 m building in Chicago. From conservation of energy, what is its speed at the bottom? • 5880 m/s • 2940 m/s • 76.7 m/s • 54.2 m/s

  39. Pendulum • At bottom, all energy is kinetic. • At top, all energy is potential. • In between, there is a mix of both potential and kinetic energy. • Bowling Ball Video

  40. Energy Content of a Big Mac • 540 Cal = 540000 cal • 1 Cal = 4186 Joules

  41. How high can we lift a 1kg object with the energy content of 1 Big Mac? • PE = mgh • h = PE/(mg) • PE = 2,260,440 J • m = 1 kg • g = 9.8 m/s2

  42. 2 Big Macs have enough energy content to lift a 1 kg object up to the orbital height of the International Space Station. • 150 Big Macs could lift a person to the same height. • It would take about 4,000,000 Big Macs to get the space shuttle to the ISS height. • Note: McDonald’s sells approximately 550,000,000 Big Macs per year.

  43. Cannon: Energy KEb= ½ mv2 = 0.5 (5kg)(400m/s)2 = 400,000 kgm2/s2 = 400,000 J KEc= ½ mv2 = 0.5 (1000kg)(2m/s)2 = 2,000 kgm2/s2 = 2,000 J Note: Cannon Ball has 200 times more ENERGY

  44. When I drop a rock, it start off with PE which gets converted in to KE as it falls. At the end, it is not moving, so it has neither PE or KE. What happened to the energy? • Energy is not conserved in this case. • The energy is converted into Thermal energy • The energy is transferred to whatever it is dropped on.

  45. Important Equations

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