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CBA Review #2 Mechanics and Thermal Physics

CBA Review #2 Mechanics and Thermal Physics. Work-Energy Momentum Conservation Impulse Thermodynamics. Work and Energy. Work = Fd Units = Joules. F = magnitude of the force d = magnitude of the displacement. A 100N force acts on a box 1.5m to the right.

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CBA Review #2 Mechanics and Thermal Physics

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  1. CBA Review #2 Mechanics and Thermal Physics Work-Energy Momentum Conservation Impulse Thermodynamics

  2. Work and Energy

  3. Work = Fd Units = Joules F = magnitude of the force d = magnitude of the displacement A 100N force acts on a box 1.5m to the right. How much work did the force do? Work = 100(1.5) = 150 J

  4. Kinetic Energy – Energy of Motion KE = (1/2)mv2 Example: Find the kinetic energy of a 20kg mass moving at 10 m/s. KE = (1/2)mv2 = (1/2)(20)(10)2 = 1000J Example: If you double your velocity, what happens to the KE? KE (new) = (1/2)m(2v)2 = 4KE(original)

  5. Work Energy Theorem Work Done = DKE or Fd = ½mvf2 – ½mvi2

  6. Example A 10.0N force acts on a 4.00kg box initially at rest. If the force pushes the box 3.00 meters, what I the final velocity of the box? Fd = ½mvf2 – ½mvi2 10(3) = (1/2)4vf2– 0 30 = (2)vf2 vf2 = 15 vf = 3.87 m/s

  7. Energy Types Stored Energy – Potential Energy Energy of Motion – Kinetic Energy

  8. Gravitational Potential Energy The work you do to lift an object is equal to its increase in gravitational PE. Work to lift = PE = mgh h = vertical distance from ground level.

  9. Example How much work does a 100kg person do walking up a flight of stairs that takes her 10m off of the ground? Work = increase in PE = mgh = 100(9.8)10 = 9800 Joules.

  10. Total Mechanical Energy, E E = KE + PE If there is no friction, the total mechanical energy is conserved. This means KE + PE is always the same number. So if KE drops, PE must rise. If PE drops, KE must rise. Another way to say this, is that KE is converted to PE, or PE is converted to KE.

  11. Conservation of Energy

  12. Example A 1 kg rock is dropped from rest from a building 20m high. Fill in the table. PE at the top is mgh = 1(9.8)(20) = 196J 0 196J 196J KE at the top is zero. 98J 196J 98J 147J 49J 196J E at the top (and everywhere) is 0 + 196J = 196J 196J 196J 0 PE at the bottom is zero…………

  13. Momentum and Energy in Collisions

  14. Definition of Momentum The symbol p stands for momentum. Momentum is the product of mass and velocity. p = mv

  15. Examples of calculating momentum A 2000kg car is moving at 30m/s. What is the momentum of the car? p = mv = (2000kg)(30 m/s) = 60,000 kg m/s A .1 kg bullet has a momentum of 50 kg m/s. How fast is it moving? v = p/m = 50/.1 = 500 m/s

  16. The Vector Nature of Momentum Momentum is a vector – it points in the same direction as the velocity. In one dimension, momentum pointing to the right is positive. Momentum pointing to the left is negative.

  17. Example: Find the momentum of each ball. Be careful of the signs! Answer: For the 3kg ball, p = 3(20) = 60 kg m/s For the 10 kg ball, p = 2(-10) = -20 kg m/s

  18. Newton’s 2nd Law in terms of Momentum Favg = maavg = mDv/Dt = (pf – pi)/ Dt = Dp/Dt FavgDt = Dp Impulse = Change in momentum

  19. Example A 50N force is applied to a 20kg particle moving at 4m/s. The force is applied for 4 seconds. 1. What is the impulse? Impulse = FDt = 50(4) = 200 N.s 2. How fast is the particle moving after 4 seconds? Impulse = Dp I = mvf – mvi 200 = 20vf - 20(4) vf= (200 + 80) /20 = 14 m/s

  20. Conservation of Momentum Momentum is Conserved for Collisions Total momentum = Total momentum before the collision after the collision Pbefore = Pafter

  21. Completely Inelastic Collisions • When two objects hit and stick together. • Or, the reverse of this – when one object breaks apart into two objects. Momentum is Conserved Total momentum = Total momentum before the collision after the collision Pbefore = Pafter

  22. Example A cannon ( mass = 500kg) fires a cannon ball ( m = 50kg) at 40m/s. How fast does the cannon move after it fires the cannon ball? Before: Pi = 0 After: Pf = mballvball + mcannonvcannon Pi = Pf 0 = mballvball + mcannonvcannon (-mballvball )/mcannon =vcannon = (-50)(40)/500 = -4 m/s

  23. Example A car mass = 1kg moving at 3m/s hits another 1kg car and they stick together. How fast are they moving after they stick together? Pi = mvi = 1(3) = 3 Pf = 2mv = 2v 2v = 3, v = 1.5 m/s

  24. Example A car mass = 10kg moving at 2m/s hits another 15kg car moving to the left at 3m/s and they stick together. How fast are they moving after they stick together? Pi = m1v1i + m2v2i = 10(2) + 15(-3) = -25 Pf = m1v1f + m2v2f = (m1 + m2 )vf = 25vf -25 = 25vf vf = -25/25 = -1 m/s

  25. Elastic Forces - Hooke’s Law F = kx PE = kx2 k =spring constant in N/m

  26. Thermodynamics • Name the three methods of heat transfer and give an example of each. • Conduction: typically through solidsThe handle of a pot also gets hot • Convection: hot gas/liquid risesConvection oven, or hot magma rises inside the core of the earth • Radiation: transfer without mediumThe sun warms the earth through space

  27. Thermodynamics • What happens to metal when heated? • Like most materials, metal expands when heated.

  28. Heat Energy, Q Heat to raise the temperature of a substance with no phase change: Q = mcDT Heat required for a change of state: Q = mL

  29. Thermodynamics • What is entropy? • Entropy is a measure of the disorder in a system. Without the input of work, the entropy of a system will always increase. The entropy of the universe is constantly increasing. For example: • Ice : • High order • Low entropy • Ice melted • Less order • Higher entropy

  30. Method of Mixtures m1c1DT1 + m2c2DT2 = 0 400g of water at 50 degrees C is mixed with 600g of water at 70 degrees C. What’s the final temperature? 400(1)(Tf -50) + 600(1)(Tf -70) = 0 1000Tf - 62000 = 0 Tf = 62 degrees C.

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