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1. 1. Physics Applied to Radiology Chapter 3 Fundamentals of Physics
2. 2. Physics <ul><li>natural science </li></ul><ul><li>deals with matter and energy </li></ul><ul><ul><li>defines & characterizes </li></ul></ul><ul><ul><li>interactions between matter and energy </li></ul></ul>
3. 3. Matter <ul><li>a physical substance </li></ul><ul><li>characteristics of all matter </li></ul><ul><ul><li>occupies space </li></ul></ul><ul><ul><li>has mass </li></ul></ul>
4. 4. Energy <ul><li>capacity for doing work </li></ul>
5. 5. Math <ul><li>exact vs. approximate numbers </li></ul><ul><ul><li>exact -- defined or counted </li></ul></ul><ul><ul><li>approximate -- measured </li></ul></ul><ul><li>examples </li></ul><ul><ul><li>your height </li></ul></ul><ul><ul><li># of chairs in room </li></ul></ul><ul><ul><li># of seconds in a minute </li></ul></ul><ul><ul><li># seconds to run 100 m dash </li></ul></ul>
6. 6. <ul><li># of digits in a value when... </li></ul><ul><ul><li>leading & trailing zeros are ignored </li></ul></ul><ul><ul><ul><li>trailing 0 may be designated as significant </li></ul></ul></ul><ul><ul><li>the decimal place is disregarded </li></ul></ul><ul><li>How many significant figures? </li></ul><ul><ul><ul><li>Value: significant figures </li></ul></ul></ul><ul><ul><ul><li>3.47 </li></ul></ul></ul><ul><ul><ul><li>0.039 </li></ul></ul></ul><ul><ul><ul><li>206.1 </li></ul></ul></ul><ul><ul><ul><li>5.90 </li></ul></ul></ul>Significant Figures
7. 7. <ul><li># of digits in a value when... </li></ul><ul><ul><li>leading & trailing zeros are ignored </li></ul></ul><ul><ul><ul><li>trailing 0 may be designated as significant </li></ul></ul></ul><ul><ul><li>the decimal place is disregarded </li></ul></ul><ul><li>How many significant figures? </li></ul><ul><ul><ul><li>Value: significant figures </li></ul></ul></ul><ul><ul><ul><li>3.47 3 </li></ul></ul></ul><ul><ul><ul><li>0.039 2 </li></ul></ul></ul><ul><ul><ul><li>206.1 4 </li></ul></ul></ul><ul><ul><ul><li>5.90 2 </li></ul></ul></ul>Significant Figures
8. 8. Accuracy vs. Precision <ul><li>accuracy -- # of significant figures </li></ul><ul><ul><ul><li>3.47 is more accurate than 0.039 </li></ul></ul></ul><ul><li>precision -- decimal position of the last significant figure </li></ul><ul><ul><ul><li>0.039 is more precise than 3.47 </li></ul></ul></ul>
9. 9. Example <ul><li>Describe the accuracy and precision of the following information. </li></ul><ul><ul><li>2.5 cm metal sheet with a .025 cm coat of paint </li></ul></ul><ul><ul><ul><li>accuracy is same for both (2 sig. fig.) </li></ul></ul></ul><ul><ul><ul><li>precision is > for paint (1/1000 vs. 1/10) </li></ul></ul></ul>
10. 10. Rounded Numbers <ul><li>all approximate # are rounded </li></ul><ul><li>last digit of approx. number is rounded </li></ul><ul><li>last sig. fig. of an approx. # is never an accurate # </li></ul><ul><li>error of last number is ½ of the last digit's place value </li></ul><ul><ul><li>(if place value is .1 then error = .05) </li></ul></ul>
11. 11. Rounded Number <ul><li>example: </li></ul><ul><ul><li>if a measured value = 32.63 </li></ul></ul><ul><ul><ul><li>error is .005 (½ of .01) </li></ul></ul></ul><ul><ul><ul><li>actual # is between </li></ul></ul></ul><ul><ul><ul><li>32.635 (32.63 + .005) </li></ul></ul></ul><ul><ul><ul><li>32.625 (32.63 - .005) </li></ul></ul></ul>
12. 12. Rounding Rules <ul><li>round at the end of the total calculation </li></ul><ul><ul><li>do not round after each step in complex calculations </li></ul></ul><ul><li>when - or + use least precise # </li></ul><ul><ul><li>(same # of decimal places) </li></ul></ul><ul><li>when x or ÷ use least accurate # </li></ul><ul><ul><li>(same # of sig. figures) </li></ul></ul>
13. 13. Rounding Example 1 <ul><li>73.2 </li></ul><ul><li>8.0627 </li></ul><ul><li>93.57 </li></ul><ul><li>+ 66.296 </li></ul><ul><li>241.1287 </li></ul><ul><li>241.1 # decimal places = to least precise value </li></ul>
14. 14. Rounding Example 2 <ul><li>2.4832 </li></ul><ul><li>x 30.51 </li></ul><ul><li>75.762432 </li></ul><ul><li>75.76 # significant figures = to least accurate number </li></ul>
15. 15. Numerical Relationships <ul><li>direct linear </li></ul><ul><ul><li>as x  y  (or vice versa) </li></ul></ul><ul><ul><li>example formula y = k x </li></ul></ul><ul><ul><li>expressed as proportion y  x </li></ul></ul><ul><ul><li>example: x y (for y = 5x) </li></ul></ul><ul><ul><li>1 5 </li></ul></ul><ul><ul><li>2 10 </li></ul></ul><ul><ul><li>3 15 </li></ul></ul>
16. 16. Numerical Relationships <ul><li>direct exponential </li></ul><ul><ul><li>direct square (or other exponent) </li></ul></ul><ul><ul><li>as x  y  by an exponential value  (or vice versa) </li></ul></ul><ul><ul><li>example formula y = k x 2 </li></ul></ul><ul><ul><li>expressed as proportion y  x 2 </li></ul></ul><ul><ul><li>example: x y (for y = 5x 2 ) </li></ul></ul><ul><ul><li>1 5 </li></ul></ul><ul><ul><li>2 20 </li></ul></ul><ul><ul><li>3 45 </li></ul></ul>
17. 17. Numerical Relationships (cont.) <ul><li>indirect </li></ul><ul><ul><li>as x  y  </li></ul></ul><ul><ul><li>example formula x y = constant </li></ul></ul><ul><ul><li>expressed as proportion y  1/x </li></ul></ul><ul><ul><li>example: x y (for xy = 100) </li></ul></ul><ul><ul><li>1 100 </li></ul></ul><ul><ul><li>2 50 </li></ul></ul><ul><ul><li>4 25 </li></ul></ul>
18. 18. Numerical Relationships (cont.) <ul><li>indirect exponential </li></ul><ul><ul><li>inverse square (or other exponent) </li></ul></ul><ul><ul><li>as x  y  by an exponential value  (or vice versa) </li></ul></ul><ul><ul><li>example formula y x 2 = constant </li></ul></ul><ul><ul><li>expressed as proportion y  1/ x 2 </li></ul></ul><ul><ul><li>example: x y (for x 2 y = 100) </li></ul></ul><ul><ul><li>1 100 </li></ul></ul><ul><ul><li>2 25 </li></ul></ul><ul><ul><li>4 6.25 </li></ul></ul>
19. 19. Graphs <ul><li>used to display relationships between 2 variables </li></ul><ul><ul><li>Y-axis (dependent) measured value </li></ul></ul><ul><ul><li>X-axis (independent) controlled value </li></ul></ul>x-axis y-axis
20. 20. Graphic Relationships ( on linear graph paper) <ul><li>slope (left to right) </li></ul><ul><ul><li>direct = ascending </li></ul></ul><ul><ul><li>indirect = descending </li></ul></ul><ul><li>shape </li></ul><ul><ul><li>linear = straight </li></ul></ul><ul><ul><li>exponential = curved </li></ul></ul>
21. 21. Evaluating Graphed Information <ul><li>identify variables </li></ul><ul><li>describe shape & slope of line </li></ul><ul><li>correlate information to theory </li></ul>
22. 22. Example #1 <ul><ul><li>Relationship of mA to Intensity </li></ul></ul>
23. 23. Example #1 (evaluated) <ul><ul><li>Relationship of mA to Intensity </li></ul></ul><ul><ul><ul><li>variables </li></ul></ul></ul><ul><ul><ul><ul><li>independent = mA </li></ul></ul></ul></ul><ul><ul><ul><ul><li>dependent = Exposure </li></ul></ul></ul></ul><ul><ul><ul><li>shape & slope </li></ul></ul></ul><ul><ul><ul><ul><li>slope = ascending (=direct) </li></ul></ul></ul></ul><ul><ul><ul><ul><li>shape = straight line (=linear) </li></ul></ul></ul></ul><ul><ul><ul><li>correlate to theory </li></ul></ul></ul><ul><ul><ul><ul><li>mA has a direct linear relationship to exposure; as mA increases exposure increases in a similar fashion; the graph demonstrates that if you double the mA (200 to 400) you also double the exposure (30 mR to 60 mR ) </li></ul></ul></ul></ul>
24. 24. Example #2 <ul><li>Relationship of the # days before exam to amount of study time </li></ul>
25. 25. Quantities & Units <ul><li>quantity = measurable property </li></ul><ul><ul><li>quantity definition (what is measured) </li></ul></ul><ul><ul><li>length distance between two points </li></ul></ul><ul><ul><li>mass amount of matter (not weight) </li></ul></ul><ul><ul><li>time duration of an event </li></ul></ul><ul><li>unit = standard used to express a measurement </li></ul><ul><ul><li>quantity unit other units </li></ul></ul><ul><ul><li>length meter </li></ul></ul><ul><ul><li>mass kilogram </li></ul></ul><ul><ul><li>time second </li></ul></ul>
26. 26. Unit Systems <ul><li>System length mass time </li></ul><ul><li>English foot slug (pound) second </li></ul><ul><li>metric SI** meter kilogram second </li></ul><ul><ul><li>** also ampere, Kelvin, mole, candela </li></ul></ul><ul><li>metric MKS meter kilogram second </li></ul><ul><li>metric CGS centimeter gram second </li></ul><ul><li>Do not mix unit systems when doing calculations!! </li></ul>
27. 27. Converting Units <ul><li>convert 3825 seconds to hours </li></ul><ul><ul><li>identify conversion factor(s) needed </li></ul></ul><ul><ul><li>factors needed: 60 sec = 1 min & 60 min = 1 hour </li></ul></ul><ul><ul><li>arrange factors in logical progression </li></ul></ul><ul><ul><ul><li>For seconds  hours </li></ul></ul></ul><ul><ul><ul><li>sec  min/sec  hour/min </li></ul></ul></ul><ul><ul><li>set up calculation </li></ul></ul>
28. 28. Dimensional Prefixes Bushong, table 2-3 (pg 23) <ul><li>used with metric unit systems </li></ul><ul><li>modifiers used with unit </li></ul><ul><li>a power of 10 to express the magnitude </li></ul><ul><li>prefix symbol factor numerical equivalent </li></ul><ul><li> tera- T 10 12 1 000 000 000 000 </li></ul><ul><li> giga- G 10 9 1 000 000 000 </li></ul><ul><li> mega- M 10 6 1 000 000 </li></ul><ul><li> kilo- k 10 3 1 000 </li></ul><ul><li> centi- c 10 -2 .01 </li></ul><ul><li> milli m 10 -3 .001 </li></ul><ul><li> micro-  10 -6 .000 001 </li></ul><ul><li> nano- n 10 -9 .000 000 001 </li></ul><ul><li> pico- p 10 -12 .000 000 000 001 </li></ul>
29. 29. Rules for Using Prefixes <ul><li>To use a prefix divide by prefix value & include the prefix with the unit </li></ul><ul><li>To remove a prefix multiply by prefix value & delete prefix notation from the unit </li></ul>
30. 30. Base Quantities & Units (SI) <ul><li>describes a fundamental property of matter </li></ul><ul><li>cannot be broken down further </li></ul><ul><li>quantity SI unit definition for quantity </li></ul><ul><li>length meter distance between two points </li></ul><ul><li>mass kilogram amount of matter (not weight) </li></ul><ul><li>time second duration of an event </li></ul>
31. 31. Derived Quantities & Units <ul><li>properties which arrived at by combining base quantities </li></ul><ul><li>quantity units definition for quantity </li></ul><ul><li>area m x m m 2 surface measure </li></ul><ul><li>volume m x m x m m 3 capacity </li></ul><ul><li>velocity m/s m/s distance traveled per unit time </li></ul><ul><li>acceleration m/s/s m/s 2 rate of change of velocity </li></ul><ul><li>ms -2 </li></ul>
32. 32. Derived Quantities with Named Units <ul><li>quantities with complex SI units </li></ul><ul><li>quantity units definition </li></ul><ul><li>frequency Hertz Hz # of ?? per second </li></ul><ul><li>force Newton N &quot;push or pull&quot; </li></ul><ul><li>energy Joule J ability to do work </li></ul><ul><li>absorbed dose Gray Gy radiation energy deposited (rad) in matter </li></ul>
33. 33. Solving Problems <ul><li>1. Determine unknown quantity </li></ul><ul><li>2. Identify known quantities </li></ul><ul><li>3. Select an equation (fits known & unknown quantities) </li></ul><ul><li>4. Set up numerical values in equation </li></ul><ul><ul><li>same unit or unit system </li></ul></ul><ul><li>5. Solve for the unknown </li></ul><ul><ul><li>write answer with magnitude & units </li></ul></ul><ul><ul><li>raw answer vs. answer in significant figures </li></ul></ul>
34. 34. Mechanics <ul><li>study of motion & forces </li></ul><ul><li>motion = change in position or orientation </li></ul><ul><li>types of motion </li></ul><ul><ul><li>translation </li></ul></ul><ul><ul><ul><li>one place to another </li></ul></ul></ul><ul><ul><li>rotation </li></ul></ul><ul><ul><ul><li>around axis of object's mass </li></ul></ul></ul>
35. 35. Measuring Quantities in Mechanics <ul><li>all have magnitude & unit </li></ul><ul><li>scalar vs. vector quantities </li></ul><ul><ul><li>Scalar -- magnitude & unit </li></ul></ul><ul><ul><li>Vector -- magnitude, unit & direction </li></ul></ul>run 2 km vs run 2 km east
36. 36. Vector Addition/Subtraction <ul><li>requires use of graphs, trigonometry or special mathematical rules to solve </li></ul><ul><li>example: </li></ul>F 1 F 2 F 1 + F 2 = Net force
37. 37. Quantities in Mechanics <ul><li>speed </li></ul><ul><ul><li>rate at which an object covers distance </li></ul></ul><ul><ul><ul><li>rate </li></ul></ul></ul><ul><ul><ul><ul><li>indicates a relationship between 2 quantities </li></ul></ul></ul></ul><ul><ul><ul><ul><li>\$/hour exams/tech # of people/sq. mile </li></ul></ul></ul></ul><ul><ul><li>speed = distance/time </li></ul></ul><ul><ul><li>speed is a scalar quantity </li></ul></ul>
38. 38. Speed (cont.) d in m t in s v = m/s same at all times total distance total time General Formula: Variations: instantaneous uniform average v at 1 point in time v = d t distance time
39. 39. Speed Example <ul><li>An e - travels the 6.0 cm distance between the anode & the cathode in .25 ns. What is the e - speed? [Assume 0 in 6.0 is significant] </li></ul><ul><ul><li>v = ?? 6.0 cm = distance .25 ns = time </li></ul></ul><ul><ul><li>v = d / t (units: m /s  need to convert) </li></ul></ul><ul><ul><li> 6.0 cm = 6.0 x 10 -2 m .25 ns = .25x10 -9 s </li></ul></ul><ul><ul><li>= 6 x 10 -2 m / .25x10 -9 s </li></ul></ul><ul><ul><li>= 2.40000 x 10 8 m/s (raw answer) </li></ul></ul><ul><ul><li>= 2.4 x 10 8 m/s (sig. fig. answer) </li></ul></ul>
40. 40. Velocity <ul><li>speed + the direction of the motion </li></ul><ul><li>vector quantity </li></ul><ul><ul><li>A boat is traveling east at 15 km/hr and must pass through a current that is moving northeast at 10 km/hr . What will be the true velocity of the boat? </li></ul></ul>
41. 41. Acceleration <ul><li>rate of change of velocity with time </li></ul><ul><ul><li>if velocity changes there is acceleration </li></ul></ul><ul><li>includes:  v  v  direction </li></ul><ul><li>formula: </li></ul> v = v f - v i units v in m/s t in s a = m/s 2 a =  v  t
42. 42. Acceleration Example <ul><li>A car is traveling at 48 m/s. After 12 seconds it is traveling at 32 m/s. What is the car’s acceleration? </li></ul><ul><ul><li>a = ? 48 m/s = v i 12 s =  t 32 m/s = v f </li></ul></ul><ul><ul><li>a =  v /  t </li></ul></ul><ul><ul><li>   v = v f - v i = 32m/s - 48 m/s = -16 m/s </li></ul></ul><ul><ul><li>a = -16m/s / 12 s = -1.3333333333 m/s 2 </li></ul></ul><ul><ul><li>= -1.3 m/s 2 [ -sign designates slowing down] </li></ul></ul>
43. 43. Application of v and a in Radiology <ul><li>KE (motion) of e- used to produce x rays </li></ul><ul><ul><li>controlling the v of e- enables the control of the photon energies </li></ul></ul><ul><li>Brems photons are produced when e - undergo a -a close to the nucleus of an atom </li></ul>
44. 44. Newton's Laws of Motion <ul><li>1. Inertia </li></ul><ul><li>2. Force </li></ul><ul><li>3. Recoil </li></ul>
45. 45. Newton's First Law <ul><li>defined -- in notes </li></ul><ul><li>inertia: resistance to a  in motion </li></ul><ul><ul><li>property of all matter </li></ul></ul><ul><ul><li>mass = a measure of inertia </li></ul></ul>
46. 46. Inertia <ul><li>Semi-trailer truck </li></ul><ul><ul><li>large mass </li></ul></ul><ul><ul><li>large inertia </li></ul></ul><ul><li>Bicycle </li></ul><ul><ul><li>small mass </li></ul></ul><ul><ul><li>small inertia </li></ul></ul>
47. 47. Newton's 2nd Law (Force) <ul><li>Force </li></ul><ul><ul><li>anything that can  object's motion </li></ul></ul><ul><ul><li>Fundamental forces </li></ul></ul><ul><ul><ul><li>Nuclear forces </li></ul></ul></ul><ul><ul><ul><ul><li>&quot;strong&quot; & &quot;weak&quot; </li></ul></ul></ul></ul><ul><ul><ul><li>Gravitational force </li></ul></ul></ul><ul><ul><ul><li>Electromagnetic force </li></ul></ul></ul>
48. 48. Mechanical Force <ul><li>push or pull </li></ul><ul><li>vector quantity </li></ul><ul><ul><li>net force = vector sum of all forces </li></ul></ul><ul><ul><li>push on box + friction from floor </li></ul></ul><ul><li>equilibrium -- net force = 0 </li></ul>Vector sum
49. 49. 2nd Law (Force) <ul><li>defined -- in notes </li></ul><ul><li>formula for the quantity “force” </li></ul><ul><ul><li>force = mass x acceleration </li></ul></ul><ul><ul><li>F = m x a </li></ul></ul>Newton N a =  v  t kg m s 2 <ul><li>units kg x m/s 2 </li></ul>
50. 50. Example Problem for 2nd Law <ul><li>What is the net force needed to accelerate a 5.1 kg laundry cart to 3.2 m/s 2 ? </li></ul><ul><ul><li>F =?? 5.1 kg = mass 3.2 m/s 2 = acceleration </li></ul></ul><ul><ul><li>F = m a </li></ul></ul><ul><ul><li>= 5.1 kg x 3.2 m/s 2 </li></ul></ul><ul><ul><li>= 16.32 kg m/s 2 </li></ul></ul><ul><ul><li>= 16 N </li></ul></ul>
51. 51. Example 2: <ul><li>A net force of 275 N is applied to a 110 kilogram mobile unit. What is the unit's acceleration? </li></ul><ul><ul><li>acceleration =?? 275 N = F 110 kg = mass </li></ul></ul><ul><ul><li>F = m a </li></ul></ul><ul><ul><li>a = F / m </li></ul></ul><ul><ul><li>= 275[kg m/s 2 ] / 110kg </li></ul></ul><ul><ul><li>= 2.5 m/s 2 </li></ul></ul>
52. 52. Example 3 <ul><li>An object experiences a net force of 376N. After 2 seconds the change in the object's velocity 15m/s. What is the object's mass? </li></ul><ul><li>mass =?? 376 N = F 2 s =  t 15 m/s =  v </li></ul><ul><ul><li>F = m a  m = F / a </li></ul></ul><ul><ul><li>a =  v/  t </li></ul></ul><ul><ul><li>= 15 m / s / 2 s = 7.5 m/s 2 </li></ul></ul><ul><ul><li>m = 376 [kg m/s 2 ] / 7.5 m/s 2 </li></ul></ul><ul><ul><li> = 50.13333333333 kg = 50 kg </li></ul></ul>
53. 53. Weight <ul><li>adaptation of Newton's 2nd law </li></ul><ul><li>weight = force caused by the pull of gravitation </li></ul><ul><ul><li>weight  mass </li></ul></ul><ul><ul><li>gravitational force inertia of the object </li></ul></ul><ul><ul><li>varies with gravity always constant </li></ul></ul><ul><ul><li>unit = N [pound] unit = kg [slug] </li></ul></ul><ul><li>when g is a constant then weight proportional mass </li></ul>
54. 54. Weight (cont.) <ul><li>formula for quantity “weight” </li></ul><ul><li> modified from force formula </li></ul><ul><ul><li>F = m x a </li></ul></ul><ul><ul><li>Wt. = m x g g earth = 9.8m/s 2 </li></ul></ul>Newton N kg m s 2 units kg x m/s 2
55. 55. Weight Problem <ul><li>What is the weight (on earth) of a 42 kg person? </li></ul><ul><ul><li>Wt. = ?? 42 kg = mass [9.8m/s 2 = gravity] </li></ul></ul><ul><ul><li>Wt. = m x g </li></ul></ul><ul><ul><li>= 42 kg x 9.8m/s 2 </li></ul></ul><ul><ul><li>= 411.6 kg m/ s 2 </li></ul></ul><ul><ul><li>= 410 N </li></ul></ul>
56. 56. Weight Problem #2 <ul><li>What is the mass of a 2287N mobile x-ray unit? </li></ul><ul><ul><li>mass = ?? 2287N = Wt [9.8m/s 2 = gravity] </li></ul></ul><ul><ul><li>Wt. = m x g </li></ul></ul><ul><ul><li>m = Wt. / g </li></ul></ul><ul><ul><li>= 2287N / 9.8m/s 2 </li></ul></ul><ul><ul><li>= 233.3673469388 kg </li></ul></ul><ul><ul><li>= 233.4 kg </li></ul></ul>
57. 57. 3rd Law (Recoil) <ul><li>Defined -- in notes </li></ul><ul><ul><li>no single force in nature </li></ul></ul><ul><ul><li>all forces act in pairs </li></ul></ul><ul><ul><ul><li>action vs. reaction </li></ul></ul></ul><ul><li>formula </li></ul><ul><ul><li>F AB = -F BA </li></ul></ul>A B
58. 58. Momentum (Linear) <ul><li>measures the amount of motion of an object </li></ul><ul><li>tendency of an object to go in straight line when at a constant velocity </li></ul><ul><li>formula </li></ul><ul><ul><li>p = m x v </li></ul></ul><ul><li>units </li></ul><ul><ul><li>= kg x m/s </li></ul></ul><ul><ul><li>= </li></ul></ul>kg m s
59. 59. Momentum vs. Mass (Inertia) <ul><li>p = m x v </li></ul><ul><li>p  m </li></ul>Direct proportional relationship  m =  p  m =  p
60. 60. Momentum vs. Velocity <ul><li>p = m x v </li></ul><ul><li>p  v </li></ul>Direct proportional relationship 50 km/hr  v =  p 100 km/hr  v =  p
61. 61. Momentum Problem <ul><li>What is the momentum of a 8.8 kg cart that has a speed of 1.24 m/s? </li></ul><ul><ul><li>p = ?? 8.8 kg = mass 1.24 m/s = velocity </li></ul></ul><ul><ul><li>p = m x v </li></ul></ul><ul><ul><li>= 8.8 kg x 1.24 m/s </li></ul></ul><ul><ul><li>= 10.912 kg m/s </li></ul></ul><ul><ul><li>= 11 kg m/s </li></ul></ul>
62. 62. Momentum Problem #2 <ul><li>What is the speed of a 3.5x10 4 kg car that has a momentum of 1.4x10 5 kg m/s? </li></ul><ul><ul><li>velocity = ?? 3.5x10 4 kg = mass 1.4x10 5 kg m/s = momentum </li></ul></ul><ul><ul><li>p = m x v </li></ul></ul><ul><ul><li>v = p / m </li></ul></ul><ul><ul><li>= 1.4x10 5 kg m/s / 3.5x10 4 kg </li></ul></ul><ul><ul><li>= 4.0 x 10 0 m/s </li></ul></ul><ul><ul><li>= 4.0 m/s </li></ul></ul>
63. 63. Conservation Laws <ul><li>Statements about quantities which remain the same under specified conditions. </li></ul><ul><li>Most Notable Conservation Laws </li></ul><ul><ul><li>Conservation of Energy </li></ul></ul><ul><ul><li>Conservation of Matter </li></ul></ul><ul><ul><li>Conservation of Linear Momentum </li></ul></ul>
64. 64. Conservation of Linear Momentum <ul><li>momentum after a collision will equal momentum before collision </li></ul><ul><li>results in a redistribution momentum among the objects </li></ul><ul><li>p 1 = p 2 </li></ul><ul><li>m 1 v 1 = m 2 v 2 </li></ul>
65. 65. Example before collision collision occurs after collision m 1 v 1 = 1 kg m/s mv = 0 mv = 0 m 2 v 2 = 1 kg m/s
66. 66. Example #2 m 1 v 1 = 5 kg m/s mv = 0 m 2 v 2 = 5 kg m/s before collision collision occurs after collision m 2 = m A + m B v 2 = v A + v B A B A B
67. 67. Work <ul><li>defined -- in notes </li></ul><ul><ul><li>measures the change a force has on an object's position or motion </li></ul></ul><ul><ul><li>If there is NO change in position or motion, NO mechanical work is done. </li></ul></ul>F d
68. 68. Work (cont.) <ul><li>formula </li></ul><ul><ul><li>Work = force x distance </li></ul></ul><ul><ul><li> W = F x d </li></ul></ul><ul><li>units = N x m </li></ul><ul><ul><li>= </li></ul></ul>kg m s 2 x m kg m 2 s 2 = Joule J =
69. 69. Example <ul><li>How much mechanical work is done to lift a 12 kg mass 8.2 m off of the floor if a force of 130 N is applied? </li></ul><ul><li>work = ?? 12 kg = mass 8.2 m = distance 130 N = force </li></ul><ul><ul><li>W = F x d </li></ul></ul><ul><ul><li>= 130 N x 8.2 m </li></ul></ul><ul><ul><li>= 1066 N m </li></ul></ul><ul><ul><li>= 1100 J (1.1 kJ) </li></ul></ul>
70. 70. Example #2 <ul><li>A 162 N force is used to move a 45 kg box 32 m. What is the work that is done moving the box? </li></ul><ul><ul><li>work = ?? 162 N = force 45 kg = mass 32 m = distance </li></ul></ul><ul><ul><li>W = F x d </li></ul></ul><ul><ul><li>= 162 N x 32 m </li></ul></ul><ul><ul><li>= 5184 N m </li></ul></ul><ul><ul><li>= 5200 J or 5.2 kJ </li></ul></ul>
71. 71. Energy <ul><li>property of matter </li></ul><ul><li>enables matter to perform work </li></ul><ul><li>broad categories </li></ul><ul><ul><li>Kinetic Energy: due to motion </li></ul></ul><ul><ul><li>Potential Energy: due to position in a force field </li></ul></ul><ul><ul><li>Rest Energy: due to mass </li></ul></ul>
72. 72. Kinetic Energy <ul><li>work done by the motion of an object </li></ul><ul><ul><li>translation, rotation, or vibration </li></ul></ul><ul><li>formula </li></ul><ul><ul><li>KE = ½ mass x velocity squared </li></ul></ul><ul><ul><li>= ½ m v 2 </li></ul></ul><ul><li>units = kg x [m/s] 2 </li></ul>kg m 2 s 2 = Joule J =
73. 73. Example <ul><li>Find the kinetic energy of a 450 kg mobile unit moving at 6 m/s. </li></ul><ul><ul><li>kinetic energy = ?? 450 kg = mass 6 m/s = velocity </li></ul></ul><ul><ul><li>KE = ½ m v 2 </li></ul></ul><ul><ul><li>= ½ x 450 kg x [6 m/s] 2 </li></ul></ul><ul><ul><li>= 8100 kg m 2 /s 2 </li></ul></ul><ul><ul><li>= 8000 J or 8 kJ </li></ul></ul>
74. 74. Potential Energy <ul><li>capacity to do work because of the object's position in a force field </li></ul><ul><li>fields </li></ul><ul><ul><li>nuclear </li></ul></ul><ul><ul><li>electromagnetic </li></ul></ul><ul><ul><li>gravitational </li></ul></ul>
75. 75. Gravitational Potential Energy <ul><li>barbell with PE </li></ul><ul><li>formula </li></ul><ul><ul><li>PE g = mass x gravity x height </li></ul></ul><ul><ul><li>= m x g x h </li></ul></ul><ul><li>units </li></ul><ul><ul><li>= kg x m/s 2 x m </li></ul></ul><ul><ul><li>= </li></ul></ul>h g m = Joule J kg m 2 s 2
76. 76. Example <ul><li>How much energy does a 460 kg mobile unit possess when it is stationed on the 3rd floor of the hospital? (42m above ground) </li></ul><ul><li>PE = ?? 460 kg = mass 42 m = height [9.8 m/s 2 = gravity] </li></ul><ul><ul><li>Pe g = m x g x h </li></ul></ul><ul><ul><li>= 460 kg x 9.8 m/s 2 x 42 m </li></ul></ul><ul><ul><li>= 189 336 kg m 2 /s 2 </li></ul></ul><ul><ul><li>= 190 000 J or 1.9x10 5 J or 190 kJ </li></ul></ul>
77. 77. Rest Mass Energy <ul><li>energy due to mass </li></ul><ul><li>Einstein's Theory </li></ul><ul><li>formula (variation of KE formula) </li></ul><ul><ul><li>E m = mass x speed of light squared </li></ul></ul><ul><ul><li>= m c 2 [ c = 3x10 8 m/s ] </li></ul></ul><ul><li>units = kg x [m/s] 2 </li></ul>kg m 2 s 2 = Joule J =
78. 78. Example <ul><li>What is the energy equivalent of a 2.2 kg object? </li></ul><ul><li>E m = ?? 2.2 kg = mass [3x10 8 m/s = speed of light] </li></ul><ul><ul><li>E m = m c 2 </li></ul></ul><ul><ul><li>= 2.2 kg x [3x10 8 m/s ] 2 </li></ul></ul><ul><ul><li>= 1.98 x 10 17 kg m 2 /s 2 </li></ul></ul><ul><ul><li> = 2.0 x 10 17 J [trailing 0 is significant] </li></ul></ul>
79. 79. Conservation Of Energy (Matter) <ul><li>Energy is neither created nor destroyed but can be interchanged </li></ul><ul><li>(Matter is neither created nor destroyed but can be interchanged) </li></ul><ul><li>Because mass has rest energy, conservation of matter & energy can be combined </li></ul>
80. 80. Power <ul><li>Rate at which work is done </li></ul><ul><ul><li>Faster work = more power </li></ul></ul><ul><li>Rate at which energy changes </li></ul><ul><ul><li>Large E  = more power </li></ul></ul>
81. 81. Power (cont.) <ul><li>formula </li></ul><ul><ul><li>power = work / time or  energy / time </li></ul></ul><ul><ul><li>P = W / t or  E / t </li></ul></ul><ul><li>units = J / s </li></ul>kg m 2 s 3 = Watt W = kg m 2 s 2 = s
82. 82. Example <ul><li>How much power is used when an 80N force moves a box 15 m during a 12 s period of time? </li></ul><ul><ul><li>(hint: solve for work first) </li></ul></ul><ul><ul><li>P = ?? 80 N = force 15 m = distance 12 s = time </li></ul></ul><ul><ul><li>P = W / t & W = F d </li></ul></ul><ul><ul><li>P = ( F d ) / t </li></ul></ul><ul><ul><li>= ( 80 N x 15 m ) / 12 s </li></ul></ul><ul><ul><li>= 100 Nm/s </li></ul></ul><ul><ul><li>= 100 W </li></ul></ul>
83. 83. Heat energy <ul><li>internal kinetic energy of matter </li></ul><ul><ul><li>from the random motion of molecules or atoms </li></ul></ul><ul><ul><li>KE & PE of molecules </li></ul></ul><ul><ul><li>heat E in matter moves from area of higher E in object to area of lower internal E </li></ul></ul><ul><li>Unit -- Calorie (a form of the joule) </li></ul><ul><ul><li>amount of heat required to raise one gram of water one degree Celsius. </li></ul></ul>
84. 84. Heat Transfer <ul><li>movement of heat energy from the hotter to cooler object (or portion of object) </li></ul><ul><li>3 methods of transfer </li></ul><ul><ul><li>conduction </li></ul></ul><ul><ul><li>convection </li></ul></ul><ul><ul><li>radiation </li></ul></ul>
85. 85. conduction <ul><li>primary means in solid objects </li></ul><ul><li>classification of matter by heat transfer </li></ul><ul><ul><li>conductors--rapid transfer </li></ul></ul><ul><ul><li>insulator--very slow to transfer </li></ul></ul>
86. 86. convection <ul><li>primary means in gasses and liquids </li></ul><ul><li>convection current--continuing rise of heated g/l and sinking of cool g/l </li></ul>
87. 87. radiation <ul><li>transfer without the use of a medium </li></ul><ul><ul><li>(i.e. no solid, liquid or gas) </li></ul></ul><ul><li>occurs in a vacuum </li></ul>
88. 88. Heat Radiation <ul><li>term “radiation” may simply refer to heat energy and not the transfer of heat </li></ul><ul><li>infra-red radiation, part of EM spectrum, is heat energy </li></ul>
89. 89. Effects of Heat Transfer <ul><li>change in physical state of matter </li></ul><ul><ul><li>solid  liquid  gas </li></ul></ul><ul><ul><li> melt boil </li></ul></ul><ul><li>change in temperature </li></ul><ul><ul><li>measure of the average KE of an object </li></ul></ul><ul><ul><li>relative measure of sensible heat or cold </li></ul></ul>
90. 90. Temperature Scales <ul><ul><li>Scales Boil (steam) Freeze (ice) No KE </li></ul></ul><ul><ul><li>Fahrenheit 212° 32° -460° </li></ul></ul><ul><ul><li>Celsius 100° 0° -273° </li></ul></ul><ul><ul><li>Kelvin (SI) 373 273 0 </li></ul></ul><ul><ul><li>1K = 1°C = 1.8°F </li></ul></ul><ul><ul><li>Conversion formulae </li></ul></ul><ul><ul><li>°F = 32 + (1.8 °C) </li></ul></ul><ul><ul><li>°C = (°F - 32)  1.8 </li></ul></ul><ul><ul><li> K = °C + 273 </li></ul></ul>