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Physics 2053C – Fall 2001

Physics 2053C – Fall 2001. Review for Final Exam http://www.hep.fsu.edu/~tadams. Important Topics. Kinematics Forces/Newton’s Laws Energy/Momentum Conservation Ideal Gases/Heat. Variable/Quantity/Units. t time s x distance m v velocity m/s a acceleration m/s 2

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Physics 2053C – Fall 2001

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  1. Physics 2053C – Fall 2001 Review for Final Exam http://www.hep.fsu.edu/~tadams Prof. Todd Adams, FSU Department of Physics

  2. Important Topics • Kinematics • Forces/Newton’s Laws • Energy/Momentum Conservation • Ideal Gases/Heat

  3. Variable/Quantity/Units t time s x distance m v velocity m/s a acceleration m/s2 F force N = kg.m/s2 E energy J = N.m P power W = J.s

  4. Kinematics • Position • Velocity – rate of change of position • Acceleration – rate of change of velocity • Constant acceleration • Constant velocity • Constant position a = 0 v = 0, a = 0

  5. Equations of Motion x = x0 + v0t + ½at2 v = v0 + at v2 = v02 + 2a(x – x0) x = position x0 = initial position v = velocity v0 = initial velocity a = acceleration t = time

  6. Forces • Force due to gravity • Normal force • Force due to friction • Tension • Buoyancy • External force (e.g. a push)

  7. Gravity • acceleration due to gravity (g = 9.80 m/s2) • force due to gravity F = mg • Weight = force due to gravity • which direction??? • Also, F = G.(m1m2)/r2 Newtons

  8. Types of Energy • Kinetic • Linear K = ½mv2 • Rotational • Potential • Gravitational U = mgh • Spring U = ½kx2 • Internal Energy • Heat Q = mcT • Work W = Fdcos

  9. Ideal Gas Law PV = nRT P = pressure (atm, bar, N/m2) V = volume (m3) n = # of moles R = gas constant T = temperature (K)

  10. How to solve FORCE problems • Read the problem. (identify what you do and don’t know, look for “hidden” knowledge) • Draw a free-body diagram (identify all forces acting upon object) • Add all forces in one direction together (x?) F = F1 + F2 + F3 + … (determine sum of forces, maybe Fnet = 0 or Fnet = ma) • Add all forces in other direction together (y?) (determine sum of forces, maybe Fnet = 0 or Fnet = ma) • Solve for what you don’t know

  11. T1 T2 M1 M2 Sample Force Problem The boxes are not moving. • What is the value of T1? • What is the value of T2? M1 = 20.0 kg M2 = 10.0 kg  = 0.3

  12. T2 T1 M1 T1 M2 Fg Sample Force Problem (cont) M1 = 20.0 kg M2 = 10.0 kg  = 0.3 F = T1 – Fg = 0 T1 = Fg T1 = M2g = (10.0 kg)(9.80 m/s2) T1 = 98.0 N M2

  13. T2 T1 M1 FN T2 T1 M2 Ffr Fg Sample Force Problem (cont) M1 = 20.0 kg M2 = 10.0 kg  = 0.3 Fy = FN – Fg = 0 FN = Fg FN = M1g = (20.0 kg)(9.80 m/s2) FN = 196.0 N M1

  14. T2 T1 M1 M2 Sample Force Problem (cont) M1 = 20.0 kg M2 = 10.0 kg  = 0.3 FN Fx = T1 – T2 – Ffr = 0 T2 = T1 - Ffr T2 = 98.0 N – (0.3)(196.0 N) T2 = 39.2 N T2 T1 M1 FN = 196.0 N Ffr Fg

  15. T1 T2 M1 M2 Sample Force Problem (cont) What if the boxes are moving with constant velocity? What if the boxes are accelerating at a = 2.2 m/s2? What if we remove T2? M1 = 20.0 kg M2 = 10.0 kg  = 0.3 T1 = 98.0 N T2 = 39.2 N

  16. How to Solve ENERGY Problems • Identify types of energy Kinetic? Gravitational Potential? Spring Potential? Heat? Internal Energy? Work? • Identify initial and final conditions • Find unknown quantities: W = K + U (if W  0) Ki + Ui = Kf + Uf (if W = 0)

  17. 5 m Sample Energy Problem A 25 kg block is released from rest 5.5 m up a frictionless plane inclined at 30o. The block slides down the incline and along a horizontal surface. The horizontal surface has a coefficient of static friction of 0.32. What is the velocity of the block at the bottom of the incline? How far along the horizontal surface will the block slide?

  18. 5 m Sample Energy Problem (cont) What kind of energies are present? Kinetic energy Gravitational potential energy Work done by friction What is the energy at A? EA = KE + PE = 0 + mgh = mgdsin = (25 kg)(9.80 m/s2)(5 m)(sin 30o) EA =612.5 J A B C

  19. 5 m Sample Energy Problem (cont) What is the energy at B? EB = EA = 612.5 J What happens to the energy as the box goes from A to B? What is the velocity at B? EB = KE + PE = ½ mvB2 + 0 vB =7.0 m/s A B C

  20. 5 m Sample Energy Problem (cont) What happens to the energy as the box goes from B to C? What is the energy at C? EC = 0.0 J How far does the box slide? W = KE + PE Wfr = Ffrd = FNd W = (0.0 J – 612.5 J) + 0 J Wfr = mgd W = Wfr . . -612.5 J = (0.32)(25 kg)(9.8 m/s2)d = (78.4 N)d . d = (612.5 J)/(78.4 N) = 7.81 m A B C

  21. How to Solve IDEAL GAS Problems PV = nRT • Identify initial and final conditions • Take ratio P1V1 n1RT1 P2V2 n2RT2 • Cancel anything which is constant • Solve for what you don’t know =

  22. Sample Problem V = 10 m/s V = 18 m/s • What are the forces on the motorcycle as it accelerates (A)? • What are the forces on the motorcycle as it moves at constant speed (B,C)? • How far does it travel while accelerating from rest to 30 m/s? • What is the kinetic energy at points A, B, C? • How much work is done by motorcycle? • How much work is done by friction getting to A, B, C? • What are the forces on the object as it moves upward from A to B? M = 250 kg 30 m F = 2500 N 25 m A B C 0 to 30 m/s in 20 s

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