Dec. 8, 2001 Prof. Todd Adams, FSU Department of Physics1 Physics 2053C – Fall 2001 Review for Final Exam

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

3 Variable/Quantity/Units ttimes xdistancem vvelocitym/s aaccelerationm/s 2 FforceN = kg. m/s 2 EenergyJ = N. m PpowerW = 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 = x 0 + v 0 t + ½at 2 v = v 0 + at v 2 = v a(x – x 0 ) x = position x 0 = initial position v = velocity v 0 = 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/s 2 ) force due to gravity F = mg Weight = force due to gravity which direction??? Also, F = G. (m 1 m 2 )/r 2 Newtons

8 Types of Energy Kinetic Linear K = ½mv 2 Rotational Potential Gravitational U = mgh Spring U = ½kx 2 Internal Energy Heat Q = mc  T Work W = Fdcos 

9 Ideal Gas Law PV = nRT P = pressure (atm, bar, N/m 2 ) V = volume (m 3 ) n = # of moles R = gas constant T = temperature (K)

10 How to solve FORCE problems 1) Read the problem. (identify what you do and don’t know, look for “hidden” knowledge) 2) Draw a free-body diagram (identify all forces acting upon object) 3) Add all forces in one direction together (x?)  F = F1 + F2 + F3 + … (determine sum of forces, maybe F net = 0 or F net = ma) 4) Add all forces in other direction together (y?) (determine sum of forces, maybe F net = 0 or F net = ma) 5) Solve for what you don’t know

11 Sample Force Problem The boxes are not moving. 1) What is the value of T 1 ? 2) What is the value of T 2 ? M1M1 M2M2 T2T2 T1T1 M 1 = 20.0 kg M 2 = 10.0 kg  = 0.3

12 Sample Force Problem (cont)  F = T 1 – F g = 0 T 1 = F g T 1 = M 2 g = (10.0 kg)(9.80 m/s 2 ) T 1 = 98.0 N M1M1 M2M2 T2T2 T1T1 M 1 = 20.0 kg M 2 = 10.0 kg  = 0.3 M2M2 FgFg T1T1

13 Sample Force Problem (cont)  F y = F N – F g = 0 F N = F g F N = M 1 g = (20.0 kg)(9.80 m/s 2 ) F N = N M1M1 M2M2 T2T2 T1T1 M 1 = 20.0 kg M 2 = 10.0 kg  = 0.3 M1M1 FgFg FNFN T1T1 T2T2 F fr

14 Sample Force Problem (cont)  F x = T 1 – T 2 – F fr = 0 T 2 = T 1 - F fr T 2 = 98.0 N – (0.3)(196.0 N) T 2 = 39.2 N M1M1 M2M2 T2T2 T1T1 M 1 = 20.0 kg M 2 = 10.0 kg  = 0.3 M1M1 FgFg FNFN T1T1 T2T2 F fr F N = N

15 Sample Force Problem (cont) What if the boxes are moving with constant velocity? What if the boxes are accelerating at a = 2.2 m/s 2 ? What if we remove T 2 ? M1M1 M2M2 T2T2 T1T1 M 1 = 20.0 kg M 2 = 10.0 kg  = 0.3 T 1 = 98.0 N T 2 = 39.2 N

16 How to Solve ENERGY Problems 1) Identify types of energy Kinetic? Gravitational Potential? Spring Potential? Heat? Internal Energy? Work? 2) Identify initial and final conditions 3) Find unknown quantities: W =  K +  U (if W  0) K i + U i = K f + U f (if W = 0)

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

18 Sample Energy Problem (cont) 5 m What kind of energies are present? Kinetic energy Gravitational potential energy Work done by friction What is the energy at A? E A = KE + PE = 0 + mgh = mgdsin  = (25 kg)(9.80 m/s 2 )(5 m)(sin 30 o ) E A = J A B C

19 Sample Energy Problem (cont) 5 m What is the energy at B? E B = E A = J What happens to the energy as the box goes from A to B? What is the velocity at B? E B = KE + PE = ½ mv B v B = 7.0 m/s A B C

20 Sample Energy Problem (cont) 5 m What happens to the energy as the box goes from B to C? What is the energy at C? E C = 0.0 J How far does the box slide? W =  KE +  PEW fr = F fr d =  F N d W = (0.0 J – J) + 0 J W fr =  mgd W = W fr J = (0.32)(25 kg)(9.8 m/s 2 )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 1) Identify initial and final conditions 2) Take ratio P 1 V 1 n 1 RT 1 P 2 V 2 n 2 RT 2 3) Cancel anything which is constant 4) Solve for what you don’t know =

22 Sample Problem 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 0 to 30 m/s in 20 s 25 m 30 m F = 2500 N V = 10 m/s V = 18 m/s A B C