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1 8/16/017 One dimensional Motion test 8/4 The Nature of Science Observation: important first step toward scientific theory; requires imagination to tell what is important. Theories: created to explain observations; will make predictions. Observations will tell if the prediction is accurate, and the cycle goes on. 1

2 8/16/017 The Nature of Science Models, Theories, and Laws Models are very useful during the process of understanding phenomena. A model creates mental pictures; care must be taken to understand the limits of the model and not take it too seriously. A theory is detailed and can give testable predictions. A law is a brief description of how nature behaves in a broad set of circumstances. A principle is similar to a law, but applies to a narrower range of phenomena.

3 8/16/017 The number of significant figures is the number of reliably known digits in a number. It is usually possible to tell the number of significant figures by the way the number is written:

4 8/16/017 Measurement and Uncertainty; Significant Figures When multiplying or dividing numbers, the result has as many significant figures as the number used in the calculation with the fewest significant figures. Example: 11.3 cm x 6.8 cm = 77 cm When adding or subtracting, the answer is no more accurate than the least accurate number used. Measurement and Uncertainty; Significant Figures No measurement is exact; there is always some uncertainty due to limited instrument accuracy and difficulty reading results. The photograph to the left illustrates this it would be difficult to measure the width of this x4 to better than a millimeter. 4

5 8/16/017 Measurement and Uncertainty; Significant Figures Estimated uncertainty is written with a ± sign; for example: Percent uncertainty is the ratio of the uncertainty to the measured value, multiplied by 100: Measurement and Uncertainty; Significant Figures When adding or subtracting numbers, you add the estimated uncertainty of each number together. When multiplying or dividing numbers, you add the percent uncertainty of each number together. 5

6 8/16/017 Go to the Physics honors page Click the link for Labs on the side menu and do the measurement lab Assignment #1 Do pg. -3 #,10,1,18,0 and complete measurement lab write up 6

7 8/16/017 One dimensional Motion test 8/4 Units, Standards, and the SI System Quantity Unit Standard Length Meter Length of the path traveled by light in 1/99,79,458 second. Time Second Time required for 9,19,631,770 periods of radiation emitted by cesium atoms Mass Kilogram Platinum cylinder in International Bureau of Weights and Measures, Paris 7

8 8/16/017 Units, Standards, and the SI System These are the standard SI prefixes for indicating powers of 10. Many are familiar; Y, Z, E, h, da, a, z, and y are rarely used. Units, Standards, and the SI System We will be working in the SI system, where the basic units are kilograms, meters, and seconds. British engineering system has force instead of mass as one of its basic quantities, which are feet, pounds, and seconds. 8

9 8/16/017 Converting Units Converting between metric units, for example from kg to g, is easy, as all it involves is powers of 10. Converting to and from British units is considerably more work. For example, given that 1 m = ft, this 8611-m mountain is 851 feet high. Bicyclists in the Tour de France reach speeds of 34.0 miles per hour (mi/h) on flat sections of the road. What is this speed in (a) kilometers per hour (km h -1 )? 34.0 mi 1hr 1.609km 1mi 54.7km/ hr (b) meters per second (m s -1 )? 54.7 km 1000m 1hr 1hr 1km 3600s 15.m / s 9

10 8/16/017 Order of Magnitude: Rapid Estimating A quick way to estimate a calculated quantity is to round off all numbers to one significant figure and then calculate. Your result should at least be the right order of magnitude; this can be expressed by rounding it off to the nearest power of 10. Diagrams are also very useful in making estimations. Dimensions and Dimensional Analysis Dimensions of a quantity are the base units that make it up; they are generally written using square brackets. Example: Speed = distance / time Dimensions of speed: [L/T] Quantities that are being added or subtracted must have the same dimensions. In addition, a quantity calculated as the solution to a problem should have the correct dimensions. 10

11 8/16/017 Trig Review Opposite sin cos tan Adjacent opposite hypotenuse adjacent hypotenuse opposite adjacent A highway is to be built between two towns, one of which lies 35.0 km south and 7.0 km west of the other. What is the shortest length of highway that can be built between the two towns, and at what angle would this highway be directed with respect to due west? x 35.0 km x = x = 80.1 km tan = 35/7 = tan -1 35/7 = 5.9 o south of west 7.0 km 11

12 8/16/017-1 Reference Frames and Displacement Any measurement of position, distance, or speed must be made with respect to a reference frame. For example, if you are sitting on a train and someone walks down the aisle, their speed with respect to the train is a few miles per hour, at most. Their speed with respect to the ground is much higher. Reference Frames and Displacement x o initial position x x x o x final position displacement 1

13 8/16/017 x o Reference Frames and Displacement.0 m x 7.0 m x 7.0m.0m 5. 0 m Reference Frames and Displacement The displacement is written: Displacement is positive. Displacement is negative. 13

14 8/16/ = 6 miles 0 miles because you end and start at the same point A whale swims due east for a distance of 6.9 km, turns around and goes due west for 1.8 km, and finally turns around again and heads 3.7 km due east. (a) What is the total distance traveled by the whale? (b) What are the magnitude and direction of the displacement of the whale? a) 6.9km+1.8km+3.7km = 1.4km b) 6.9km-1.8km+3.7km = 8.8km due east 14

15 8/16/017 Average speed is the distance traveled divided by the time required to cover the distance. Average speed Distance Elapsed time SI units for speed: meters per second (m/s) Speed is always a positive value Average velocity is the displacement divided by the elapsed time. Average v Displacement velocity Elapsed time x t x t o o x t SI units for velocity: meters per second (m/s) Velocity can be a positive or a negative value depending on which direction the motion is going 15

16 8/16/017 The Space Shuttle travels at a speed of about 7.6 x 10 3 m/s. The blink of an astronaut s eye lasts about 110 ms. How many football fields (length 91.4 m) does the Shuttle cover in the blink of an eye? Distance Average speed Elapsed time 7600m/s x.110 s 836m x 836m 91.4m 9.1football fields Path C because that is the path with the longest distance traveled 16

17 8/16/017 B, C, A A, B=C Book Assignment #1 Do pg #,8,14,18,3 And pg #1,5,9,1,16 Read pg

18 8/16/017 One dimensional Motion test 8/4 The notion of acceleration emerges when a change in velocity is combined with the time during which the change occurs. 18

19 8/16/017 Acceleration A sprinter explodes out of the starting block with an acceleration of 1.3 m/s, which she sustains for 1. s. Then, her acceleration drops to zero for the rest of the race. What is her velocity (a) at t = 1. s and (b) at the end of the race? a) (1.3 m/s )(1. s) 15 m/s b) The velocity is thesame as "a" since there is no acceleration after theinitial 1. seconds 19

20 8/16/017 Acceleration Acceleration is a vector, although in onedimensional motion we only need the sign. Read the following statements and indicate the direction (right, left, up, down, east, west, north or south) of the acceleration vector. a. A car is moving eastward along Lake Avenue and increasing its speed from 5 mph to 45 mph. East (same direction as motion) b. A northbound car skids to a stop to avoid a reckless driver. South (opposition direction of motion) c. An Olympic diver slows down after splashing into the water. Down (opposition direction of motion) d. A southward-bound free kick delivered by the opposing team is slowed down and stopped by the goalie. North (opposition direction of motion) e. A downward falling parachutist pulls the chord and rapidly slows down. Up (opposition direction of motion) f. A rightward-moving Hot Wheels car slows to a stop. Left (opposition direction of motion) g. A falling bungee-jumper slows down as she nears the concrete sidewalk below. Up (opposition direction of motion) 0

21 8/16/017 Acceleration There is a difference between negative acceleration and deceleration: Negative acceleration is acceleration in the negative direction as defined by the coordinate system. Deceleration occurs when the acceleration is opposite in direction to the velocity. PHET graphing activity with Moving Man Instructions are on the class website in the Labs section. Start with the prelab and attempt to answer the questions. After you complete the activity revisit the prelab questions and make corrections to them. 1

22 8/16/017 One dimensional Motion test 8/4 Velocity Slope x t 8 m s 4m s

23 8/16/ m Velocity 1 m s 00 s Velocity 0 m/s 400 m Velocity 1 1m s 400 s Instantane ous Velocity Slope x t 6 m 5.0 s 5.m s 3

24 8/16/017 Accelerati on Slope v t 1 m s s 6m s A, B, C 4

25 8/16/ m Velocity Slope at 7.0s Slope of line B 3.0m s 5.0 s Acceleration at 7.0s is 0 m/s because it is a constant velocity The lines have different slopes and therefore have different velocities. The speeds will be the same at s The tangent line to curve A at seconds will be equal to the slope of line B 5

26 8/16/017 The displacement, x, is the area beneath the v vs. t curve. Assignment Do pg #17,1,5,6,8,35,39, 4,45,53 Read pg

27 8/16/017 One dimensional Motion test 8/4 Five kinematic variables: 1. displacement, x. acceleration (constant), a 3. final velocity (at time t), v 4. initial velocity, v o 5. elapsed time, t 7

28 8/16/017 Equations of Kinematics for Constant Acceleration v v x 1 o v at o vt v vo ax x vot 1 at.4 Equations of Kinematics for Constant Acceleration A boat travelling at +6.0m/s accelerates at a rate of +.0m/s for 8.0 seconds. How far does the boat travel during that period of acceleration? x v o t m s8.0 s.0m s 8.0 s 110 m at 8

29 8/16/017 Catapulting a Jet Find its displacement. v 6 v o 0 ax x x 6m (31) x v o 0m s x?? a 31m s v 6m s An Accelerating Spacecraft A spacecraft is traveling with a velocity of +350 m/s. Suddenly the retrorockets are fired, and the spacecraft begins to slow down with an acceleration whose magnitude is 10.0 m/s. What is the velocity of the spacecraft when the displacement of the craft is +15 km, relative to the point where the retrorockets began firing and how long does it take to reach that point? v v v v o 350 ax v 500 m/s v o ( 10)(15000) 350m s x m a 10m s v? 9

30 8/16/017 In the absence of air resistance, it is found that all bodies at the same location above the Earth fall vertically with the same acceleration. If the distance of the fall is small compared to the radius of the Earth, then the acceleration remains essentially constant throughout the descent. This idealized motion is called free-fall and the acceleration of a freely falling body is called the acceleration due to gravity. g = 9.8 m/s but 10.0 m/s is acceptable 30

31 8/16/017 A stone is dropped from the top of a tall building. After 3.00s of free fall, what is the displacement y of the stone? v o 0m s y?? a 9.8m s t 3.00 s y v t o y at y 44.1m ( 9.8)(3) or 44.1m from the top of the building Assignment Do pg #6,35,39,4,45,53 Read pg

32 8/16/017 One dimensional Motion test 8/4 In the absence of air resistance, it is found that all bodies at the same location above the Earth fall vertically with the same acceleration. If the distance of the fall is small compared to the radius of the Earth, then the acceleration remains essentially constant throughout the descent. This idealized motion is called free-fall and the acceleration of a freely falling body is called the acceleration due to gravity. g = 9.8 m/s but 10.0 m/s is acceptable 3

33 8/16/017 v o 0m s y -15m a 9.8m s v? v v v v o 0 ( 9.8)( 15) 94 v 17 m/s ay Does the pellet in part b strike the ground beneath the cliff with a smaller, greater, or the same speed as the pellet in part a? 33

34 8/16/017 When something is thrown upward and returns to the thrower, this is very symmetric. The object spends half its time traveling up; half traveling down. Velocity when it returns to the ground is the opposite of the velocity it was thrown upward with. Acceleration is 9.8 m/s everywhere! v o 35m s y?? a 9.8m s v 0 m/s v v o 0 35 ay ( 9.8)( y) y y 63 m 34

35 8/16/017 Assignment Reaction Time activity on the class website Equations of Kinematics for Constant Acceleration v v o at x 1 v x vot o vt v vo ax 1 at 35

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