Physical Science Unit: Motion

1. Physical ScienceUnit: Motion

2. Physics: A branch of Physical science that deals with physical changes of objects. The models on which Physics is based are most frequently expressed in mathmatical equations that describe the conditions of the real world. The primary task in studying physics is to understand its basic principles

3. Motion Is a change in position relative to a frame of reference Motion is measured by distance and time.

4. Frame of reference The object or point from which movement is determined Movement can only be measured with reference to something that is assumed to be fixed in place

5. The most common frame of reference is the Earth

6. Are You Moving ? • You are sitting down, reading a book…. • Are you moving? • Object is in motion when its distance from another object is changing. • All depends on the “Point of Reference” • Therefore object is in motion if it changes position relative to a reference point.

7. International System of Units • “SI” • Based on the number 10 • Distance (length) uses meter (about 39 inches) • Mass (how much matter) uses gram ( a nickel is about 5 grams) • Volume (how much space) • Liquid volume – uses liter ( a little more than a quart) • Solid volume – uses cm3( about the size of a sugar cube) • 1 ml = 1 cm3 • Weight (affect gravity has on object) uses newton ( an apple weighs about 1 newton) (1 pound is about 4.4 newtons) • Density = Mass / Volume = grms / ml

8. To Amplify the Point • Distances can be short or very long. • Basic metric unit of length is the meter. • Metric prefixes are based on the number 10. • 10 meters = 1 decameter • 10 decameters = 1 hectometer • 10 hectometer = 1 kilometer • Therefore : 1 kilometer =1000 meters • And… • There are 10 decimeters in a meter • There are 10 centimeters in a decimeter • There are 10 millimeter in a centimeter • Therefore: 1000 millimeters = 1 meter

9. Metric Stairs • You should be comfortable with converting from [cm] to [m], [mm] to [km], and so on. Convert: 1527 centigrams into hectograms: going four steps up means you move the decimal 4 places to the left. Therefore: 1527 centigrams = .1527 hectograms & 9.8712345 kg = (steps to the right) 9871234.5 mg

10. Graphing ( x,y ) coordinates • A graph w/ points (2,3) , (-2,1) & (1.5, -1) plotted: Remember: b. The y axis is vertical axis c. The origin is (0,0) Remember: a. the x axis is the horizontal axis

11. More Graphing! • Graph the following points:a) (3, 3)b) (- 2, 3)c) (- 1, - 2)d) (3, 0)e) (0, 0)f) (0, - 4) b a e d c f

12. & Still More Graphing…. • What are the coordinates of these points? Click for the answers… a. (2, 0)b) (0, 2) c) (4, 3) d) (-1, 3)e) (-3, 3) f) (-1, -3) g) (-3, -1) h) (2, -4)

13. Working w/ Units • Determining the correct units in a problem is just as important as getting the number correct. • Remember we can “cancel” numerators & denominators to make the math easier: • 24 x 6 x 2 x 9 x 18 = 24 x 6 x 2 x 9 x 18 = 1 12 x 18 x 3 x 3x 24 12 x 18 x 3 x 3 x 24 We can do the same w/ units….

14. Multiplying & Dividing Units • Do this problem: 5 minutes x 3 feet = 15 minute feet • Do this problem: 12 miles 4 miles 3 hours hour • Do this problem: mile x week x dollar x bananas x week x newton x week dollar x newton x mile x bananas x week x kilogram x week mile x week x dollar x bananas x week x newton x weekweek dollar x newton x mile x bananas x week x kilogram x week kilometer

15. Speed = distance / time • Formula: S=D/T • What is the speed of a car that traveled 75 km in 1.5 hr? S = D / T = 75km / 1.5 hr = 50 km/hr Since distance is measured in meters or kilometers and time is measured in seconds or hours, the units of speed are meters per second (m/sec) or kilometers per hour (km/hr) In Physics, distance can be thought of as having a directions. The distance is called displacement.

17. Graphing Acceleration • You can use both a speed - versus - time graph and a distance - versus - time graph to analyze the motion of an accelerating object.

18. Speed - Versus - Time Graph • The slope of a line on a speed - versus - time graph represents acceleration.

19. Distance - Versus - Time Graph • You can also show the motion of an accelerating object with a distance - versus - time graph.

20. Constant Speed • Speed that does not change. • Slope: The slant of a line connecting 2 points that indicates the change in the y axis as compared to the change in the x axis

21. Graphing line slopes (rise/run) 2 1 (2,3) (1,1) 1. Graph the line which passes through (2, 3) and has a slope of 2/3. 2. Graph the line which passes through (1, 1) and has a slope of -4. (remember - 4 = -4/1)

22. Graphing points & slope (rise/run) 2 1 (0,2) (-1,1) 1. Graph the line which passes through (0, 2) and has a slope of 3. (remember 3 can be written as 3/1) 2. Graph the line which passes through (- 1, 1) and has a slope of – 2/3.

23. Notice the difference in the graphs for constant speed and for average speed

24. Average Speed • The measure of speed obtained by dividing the total distance by the total time. • The speed of a moving objet is not always constant • Speed that changes is not constant speed • Dividing the total distance by the total time gives the average speed NOT the actual speed at that instance

25. Average Speed or Average Velocity • Average speed = total distance / total time What is the average speed after 2 minutes? total distance is 75m, total time is 2 minutes. S = D/T S = 75m / 2min S= 37.5 m/min What is the average speed between 2 & 4 minutes? total distance: 110m – 75m = 35m total time: 4min – 2min = 2minutes total time S = D/T S = 35m / 2min S= 17.5 m/min

26. Example Problem : Speed • A truck travels to and from a stone quarry that is located 2.5 km to the east. What is its distance? What is its displacement? • Solution: • Distance = 5 km, • Displacement = 0 km

27. Example Problem average acceleration • During a race, a sprinter increases from 5.0 m/s to 7.5 m/s over a period of 1.25 s. What is the sprinter’s average acceleration during this period? • Solution: • (7.5 -5)/ 1.25= • 2.0 m/s2

28. Example Problem average speed • A cross-country runner runs 10 km in 40 minutes. What is his average speed? • Solution: • Average speed = total distance / total time • 10 km/40 min • = 0.25 km / m

29. Example Problem Speed • James rode his bike 0.65 hours and traveled 8.45 km. What was his speed? • Solution: • Speed = distance /time • 0.65 hr = t • 8.45 km = d • s = d/t • s = 8.45/0.65 • s = 13 km/hr

30. Example Problem Speed • Brittany drove at a speed of 85 km / hr south for 4 hours. How far did she travel? • Solution: • Speed = distance/ time • 85 km / hr = s • 4 hrs = t • ? = d • s = d/t • 85 km/hr = d / 4 hrs • d = 340 km

31. Example Problem Velocity • A dog travels 250 meters east in 8 seconds. What is the velocity of the dog? • Solution: • 250 m = d • 8 s = t • ? = v • v = d/t • v = 250 / 8 • v = 2.5 ,/s

32. Example Problem Acceleration • 8. A runner went from 6 m/s to 2 m/s in 2 seconds, what was his acceleration? • Solution: 6 m/s = vi 2 m/s = vf 2 s = t ? = a a = vf - vi / t a = 2 – 6 / 2 a = -2 m/s2

33. Example Problem Speed • A high speed train travels with an average speed of 227 km/h. The train travels for 2 h. How far does the train travel? • Solution: • d = s ´ t = 227 km/h ´ (2.00 h) = 454 km

34. Example Problem Speed • A dog travels north for 18 meters, east for 8 meters, south for 27 meters and then west for 8 meters. What is the distance the dog traveled and what is the displacement of the dog • Solution: • distance = 61 m • displacement = 9 meters south

35. Example problem • The driver of a pickup truck drove at a velocity of 75.0 km/m for 33 minutes. What distance did the bus travel? • Solution: • 75 km / m = v • 33 m = t • ?= d • v = d/t • d = 75 x 33 • d = 2475 km

36. Velocity Velocity is speed with a direction • Written like: 125 miles/hour east or 83 m/sec towards the house • What is the velocity of a jet that traveled 1623 mi North in 83 min? • V = D / T = 1623 mi / 83 min = 19.5 mi/min North

37. Velocity • The velocities that have the same direction combine by addition: • Ex you are rowing downstream at 6 km/hr and the velocity of the river is 10 km/hr. You are actually moving at 16 km/hr

38. Velocity • Velocities that have opposite directions combine by subtraction • Ex You are rowing upstream at 10km/hr and the velocity of the river is 8km/hr. You are acturally moving at 2km/hr

39. Velocity • This idea is important in launching rockets • Rockets are launched in the same direction as the earth rotates ( about 1800 km/hr) • Thus the rocket engines and the Earth’s rotational speed work together to break the Earth’s gravitational force

40. Acceleration • The change in speed or velocity over time • In scientific community, the symbol for “change” is the triangle: • Change in velocity is found by subtracting the final speed from the initial speed Vf - Vi = V The formula for acceleration is: A = Vf - Vi= V time time Therefore the units for acceleration are going to be a distance/time/time Example ft/min/sec

41. Acceleration • For an object to accelerated it must: • Speed up (positive acceleration) • Slow down (negative acceleration a.k.a deceleration ) • Change direction of travel 3 1 2 Each of these pictures depicts a type of acceleration: 1: the shuttle is speeding up every sec of the flight into orbit 2. the horse has come to a screeching halt (slowing down) 3. the baseball thrown to the batter is hit into the outfield (changed direction)

42. What’s it mean? • What does a = 5 [m/sec2] mean? • If an object starts at rest, its velocity increases by 5 [m/sec] every second. Therefore, an object accelerating at 5m/sec2 will be travelling at 20 m/sec after 4 seconds.

43. Acceleration Problems: • Calculate acceleration for the following data: A = 60km/hr - 20 km/hr = 4 km/hr 10 sec sec A = 150km/sec - 50 km/sec = 20 km 5 sec sec2 A = 1200km/hr - 25 km/hr = 587.5 km/hr 2 min min

44. Circular Motion • Acceleration is a change in velocity • Remember velocity expresses direction as well as speed • An object in circular motion is accelerating even though its speed may be constant • Acceleration that is directed toward the center of a circular path is called centripetal acceleration

45. Centripetal Acceleration

46. Momentum • All moving objects have momentum • Momentum is equal o the mass of an object multiplied by its velocity. • Momentum = mass x velocity

47. Momentum • An objects momentum depends on both its mass and velocity • Ex stopping distance of a car is directly related to its momentum ( how fast it is moving and the mass of the car)

48. Momentum • Momentum = mass x velocity • For some reason, maybe because mass is designated as “m” in formulas, momentum is designated as “p”. • Therefore: p = mv • The unit for mass is kg, the unit for velocity is meter/second, therefore the unit for momentum is kg m/sec • Conservation of Momentum: • When two or more objects interact (collide) the total momentum before the collision is equal to the total momentum after the collision

49. Momentum – 2 moving objects During this collision the speed of both box cars changes. The total momentum remains constant before & after the collision. The masses of both cars is the same so the velocity of the red car is transferred to the blue car.

50. Momentum – 1 moving object During this collision the speed red car is transferred to the blue car. The total momentum remains constant before & after the collision. The masses of both cars is the same so the velocity of the red car is transferred to the blue car.