Kinematics Part I: Motion in 1 Dimension

Transcription

1 Kinematics Part I: Motion in 1 Dimension Lana Sheridan De Anza College Sept 26, 2017

2 Last time introduced the course

3 Overview basic ideas about physics units and symbols for scaling units motion in 1-dimension kinematic quantities graphs

4 What is Physics? Physics is the science of fundamental interactions of matter and energy.

5 What is Physics? Physics is the science of fundamental interactions of matter and energy. Physicists (and others who use physics) want to predict accurately how an object or collection of objects will behave when interacting. Why? to better understand the universe to build new kinds of technology (engines, electronics, imaging devices, mass manufacturing, energy sources) to build safer and more efficient infrastructure to go new places and explore to prepare for the future

6 What is Physics? Physics is the science of fundamental interactions of matter and energy. How is it done? Make a simplified model of the system of interest, then apply a principle to make a quantitative prediction.

7 What is Physics? Physics is the science of fundamental interactions of matter and energy. How is it done? Make a simplified model of the system of interest, then apply a principle to make a quantitative prediction. System Any physical object or group of objects about which we would like to make quantitative predictions.

8 What is Physics? Physics is the science of fundamental interactions of matter and energy. How is it done? Make a simplified model of the system of interest, then apply a principle to make a quantitative prediction. System Any physical object or group of objects about which we would like to make quantitative predictions. eg. a pool table. The system might include the balls, the sides of the table, but maybe not the whole Earth. And certainly not the Andromeda galaxy.

9 What is Physics? Model A simplified description of a system and its interactions that includes only what is necessary to make predictions.

10 What is Physics? Model A simplified description of a system and its interactions that includes only what is necessary to make predictions. eg. the billiard balls are made up of atoms, but we can make very accurate predictions about their motion and collisions by just pretending they are uniform rigid spheres.

11 What is Physics? Model A simplified description of a system and its interactions that includes only what is necessary to make predictions. eg. the billiard balls are made up of atoms, but we can make very accurate predictions about their motion and collisions by just pretending they are uniform rigid spheres. Hypothesis An educated guess about a relationship between measurable quantities. It must be falsifiable by observations or experiments.

12 What is Physics? Theory A refined quantitative model for making predictions that has been verified by multiple groups of researchers and is understood to have some regime of validity.

13 What is Physics? Theory A refined quantitative model for making predictions that has been verified by multiple groups of researchers and is understood to have some regime of validity. eg. Newtonian Mechanics - very accurately predicts the motion of billiard balls and the motion of planets, but not the perihelion precession of Mercury, and not the behavior of electrons in atoms.

14 What is Physics? Theory A refined quantitative model for making predictions that has been verified by multiple groups of researchers and is understood to have some regime of validity. eg. Newtonian Mechanics - very accurately predicts the motion of billiard balls and the motion of planets, but not the perihelion precession of Mercury, and not the behavior of electrons in atoms. Valid when v << c, gravitational fields are not too strong, distances are much bigger than l p (Planck length), etc.

15 What is Physics? Law A pattern in nature that can be described very concisely, often in a single mathematical equation.

16 What is Physics? Law A pattern in nature that can be described very concisely, often in a single mathematical equation. eg. F = m a ( If I push this shopping cart twice as hard, it will accelerate twice as fast. )

17 Question In science, a theory is (A) an educated guess. (B) less than a fact. (C) a synthesis of a large body of well-tested knowledge. (D) unchangeable.

18 Question In science, a theory is (A) an educated guess. (B) less than a fact. (C) a synthesis of a large body of well-tested knowledge. (D) unchangeable.

19 Question A scientific hypothesis may turn out to be right or it may turn out to be wrong. If it is a valid hypothesis, there must be a test that could prove it (A) right. (B) wrong.

20 Question A scientific hypothesis may turn out to be right or it may turn out to be wrong. If it is a valid hypothesis, there must be a test that could prove it (A) right. (B) wrong.

21 Quantities, Units, Measurement If we want to make quantitative statements we need to agree on measurements: standard reference units. We will mostly use SI (Système International) units: Length Mass Time meter, m kilogram, kg second, s

22 Quantities, Units, Measurement If we want to make quantitative statements we need to agree on measurements: standard reference units. We will mostly use SI (Système International) units: Length Mass Time meter, m kilogram, kg second, s Make sure you include units! Also, units can be helpful for checking that your equation is correct.

23 Defining Units Originally, units were arbitrary. Physicists now strive to chose definitions for units that are based on fundamental physical phenomena - things anyone, anywhere could in principle observe consistently.

24 Units: Length The meter, m, is the SI unit of length. It is about 3.28 feet. Originally (in 1793) the meter was defined so that the distance from the North Pole to the equator would be 10 million meters. However, this is not any easy distance to measure. In 1799 a physical bar was made that was officially declared to have marks on it 1 meter apart.

25 Units: Length The meter, m, is the SI unit of length. It is about 3.28 feet. Originally (in 1793) the meter was defined so that the distance from the North Pole to the equator would be 10 million meters. However, this is not any easy distance to measure. In 1799 a physical bar was made that was officially declared to have marks on it 1 meter apart. The current definition of the meter (since 1983) is more precise and more convenient for experiments: meter One meter is the distance light travels in 1/299,792,458-ths of a second.

26 Units: Time The SI unit of time is the second, s. The second was originally defined (via the minute and hour) as 1/86,400-th of a day.

27 Units: Time The SI unit of time is the second, s. The second was originally defined (via the minute and hour) as 1/86,400-th of a day. It is now more precisely defined in terms of the behavior of Cesium atoms. (Rubiduim and other elements are also used.)

28 Units: Time The second is now more precisely defined in terms of the behavior of Cesium atoms. (Rubiduim and other elements are also used.) Devices used to measure time this way are called atomic clocks. They are accurate to 1 second in 100 million years. 1 Atomic clock FOCS-1, METAS, Bern, Switzerland; Chip photo, NIST.

29 Units: Time The second is now more precisely defined in terms of the behavior of Cesium atoms. (Rubiduim and other elements are also used.) Devices used to measure time this way are called atomic clocks. They are accurate to 1 second in 100 million years. second One second is the time for the radiation corresponding to the transition between the two hyperfine energy levels of the ground state of the caesium-133 atom to complete 9,192,631,770 oscillations.

30 Units: Mass The kilogram, kg, is the SI unit of mass. Loosely speaking, mass is a measure of the amount of matter in an object. The kilogram currently does not have a definition in terms of natural phenomena. Originally, the gram was defined to be the mass of one cubic centimeter of water at the melting point of water.

31 Units: Mass Now the official 1-kilogram sample, the international prototype kilogram is a cylinder of platinum and iridium stored near Paris. An alternative definition of the kilogram in terms of a fundamental constant (the Planck constant) has been proposed and at some point may be adopted. 1 A replica of the prototype kilogram, Wikipedia, user Japs 88.

32 Scale of Units Scale Prefix zetta peta teragigamegakilohectodeka decicentimillimicronanopicofemto- Symbol Z P T G M k h da d c m µ n p f

33 Units are Useful: Dimensional Analysis Which of the following equations are dimensionally correct? (1) v f = v i + ax (2) y = (2 m) cos(kx), where k = 2 m 1. 1 Serway & Jewett, Page 16, # 9.

34 Units are Useful: Dimensional Analysis (1) Units of v f = v i + ax: [ms 1 ] = [ms 1 ] + [ms 2 ] [m]

35 Units are Useful: Dimensional Analysis (1) Units of v f = v i + ax: [ms 1 ] = [ms 1 ] + [ms 2 ] [m] [ms 1 ] = [ms 1 ] + [m 2 s 2 ] No. (1) is not dimensionally correct.

36 Units are Useful: Dimensional Analysis (2) Units of y = (2 m) cos(kx) [m] = [m] cos([m 1 ] [m]) [m] = [m] Yes. (2) is dimensionally correct.

37 Kinematics: Motion in 1 Dimension First we consider particles constrained to move only along a straight line, forwards or backwards.

38 Vectors scalar A scalar quantity indicates an amount. It is represented by a real number. (Assuming it is a physical quantity.)

39 Vectors scalar A scalar quantity indicates an amount. It is represented by a real number. (Assuming it is a physical quantity.) vector A vector quantity indicates both an amount and a direction. It is represented by a real number for each possible direction, or a real number and (an) angle(s). (Assuming it is a physical quantity.)

40 Notation for Vectors In the lecture notes vectors are represented using bold variables. Example: k is a scalar x is a vector In the textbook and in writing, vectors are often represented with an over-arrow: x The magnitude of a vector, x is written: x = x

41 Position Some Quantities position x displacement x (or sometimes just x) distance d Going between 2 points: Distance is the length of a path that connects the two points. Displacement is the length, together with the direction, of a straight line that connects the two points.

42 Position Some Quantities position x displacement x (or sometimes just x) distance d Position and displacement are vector quantities. Position and displacement can be positive or negative numbers. Distance is a scalar. It is always a positive number.

43 Position Some Quantities position x displacement x (or sometimes just x) distance d Position and displacement are vector quantities. Position and displacement can be positive or negative numbers. Distance is a scalar. It is always a positive number.

44 Position Some Quantities position x displacement x (or sometimes just x) distance d Position and displacement are vector quantities. Position and displacement can be positive or negative numbers. Distance is a scalar. It is always a positive number. Units: meters, m

45 Table 2.1 Position of the Car at Various Times Position t (s) x (m) vs. Time Graphs origin of coordinates (see Fig. 2.1a). It continues moving to the left and is more than 50 m to the left of x 5 0 when we stop recording information after our sixth data point. A graphical representation of this information is presented in Figure 2.1b. Such a plot is called a position time graph. Notice the alternative representations of information that we have used for the motion of the car. Figure 2.1a is a pictorial representation, whereas Figure 2.1b is a graphical representation. Table 2.1 is a tabular representation of the same information. Using an alternative representation is often an excellent strategy for understanding the situation in a given problem. The ultimate goal in many problems is a math- The car moves to the right between positions and. x (m) x (m) a The car moves to the left between positions and. x (m) t b x t (s) Figures from Serway & Jewett Figure 2.1 A car moves back and forth along a straight line. Because we are interested only in the car s translational motion, we can model it as a particle. Several representations of the information about the motion of the car can be used. Table 2.1 is a tabular representation of the information. (a) A pictorial representation of the motion of the car. (b) A graphical representation (position time graph) of the motion of the car.

46 Table 2.1 Position of the Car at Various Times Position t (s) x (m) vs. Time Graphs origin of coordinates (see Fig. 2.1a). It continues moving to the left and is more than 50 m to the left of x 5 0 when we stop recording information after our sixth data point. A graphical representation of this information is presented in Figure 2.1b. Such a plot is called a position time graph. Notice the alternative representations of information that we have used for the motion of the car. Figure 2.1a is a pictorial representation, whereas Figure 2.1b is a graphical representation. Table 2.1 is a tabular representation of the same information. Using an alternative representation is often an excellent strategy for understanding the situation in a given problem. The ultimate goal in many problems is a math- The car moves to the right between positions and. x (m) x (m) a The car moves to the left between positions and. x (m) t b x t (s) Figures from Serway & Jewett Figure 2.1 A car moves back and forth along a straight line. Because we are interested only in the car s translational motion, we can model it as a particle. Several representations of the information about the motion of the car can be used. Table 2.1 is a tabular representation of the information. (a) A pictorial representation of the motion of the car. (b) A graphical representation (position time graph) of the motion of the car.

47 Table 2.1 Position of the Car at Various Times Position t (s) x (m) vs. Time Graphs origin of coordinates (see Fig. 2.1a). It continues moving to the left and is more than 50 m to the left of x 5 0 when we stop recording information after our sixth data point. A graphical representation of this information is presented in Figure 2.1b. Such a plot is called a position time graph. Notice the alternative representations of information that we have used for the motion of the car. Figure 2.1a is a pictorial representation, whereas Figure 2.1b is a graphical representation. Table 2.1 is a tabular representation of the same information. Using an alternative representation is often an excellent strategy for understanding the situation in a given problem. The ultimate goal in many problems is a math- The car moves to the right between positions and. x (m) x (m) a The car moves to the left between positions and. x (m) t b x t (s) Figures from Serway & Jewett Figure 2.1 A car moves back and forth along a straight line. Because we are interested only in the car s translational motion, we can model it as a particle. Several representations of the information about the motion of the car can be used. Table 2.1 is a tabular representation of the information. (a) A pictorial representation of the motion of the car. (b) A graphical representation (position time graph) of the motion of the car.

48 Table 2.1 Position of the Car at Various Times Position t (s) x (m) vs. Time Graphs origin of coordinates (see Fig. 2.1a). It continues moving to the left and is more than 50 m to the left of x 5 0 when we stop recording information after our sixth data point. A graphical representation of this information is presented in Figure 2.1b. Such a plot is called a position time graph. Notice the alternative representations of information that we have used for the motion of the car. Figure 2.1a is a pictorial representation, whereas Figure 2.1b is a graphical representation. Table 2.1 is a tabular representation of the same information. Using an alternative representation is often an excellent strategy for understanding the situation in a given problem. The ultimate goal in many problems is a math- The car moves to the right between positions and. x (m) x (m) a The car moves to the left between positions and. x (m) t b x t (s) Figures from Serway & Jewett Figure 2.1 A car moves back and forth along a straight line. Because we are interested only in the car s translational motion, we can model it as a particle. Several representations of the information about the motion of the car can be used. Table 2.1 is a tabular representation of the information. (a) A pictorial representation of the motion of the car. (b) A graphical representation (position time graph) of the motion of the car.

49 Table 2.1 Position of the Car at Various Times Position t (s) x (m) vs. Time Graphs origin of coordinates (see Fig. 2.1a). It continues moving to the left and is more than 50 m to the left of x 5 0 when we stop recording information after our sixth data point. A graphical representation of this information is presented in Figure 2.1b. Such a plot is called a position time graph. Notice the alternative representations of information that we have used for the motion of the car. Figure 2.1a is a pictorial representation, whereas Figure 2.1b is a graphical representation. Table 2.1 is a tabular representation of the same information. Using an alternative representation is often an excellent strategy for understanding the situation in a given problem. The ultimate goal in many problems is a math- The car moves to the right between positions and. x (m) x (m) a The car moves to the left between positions and. x (m) t b x t (s) Figures from Serway & Jewett Figure 2.1 A car moves back and forth along a straight line. Because we are interested only in the car s translational motion, we can model it as a particle. Several representations of the information about the motion of the car can be used. Table 2.1 is a tabular representation of the information. (a) A pictorial representation of the motion of the car. (b) A graphical representation (position time graph) of the motion of the car.

50 Table 2.1 Position of the Car at Various Times Position t (s) x (m) vs. Time Graphs origin of coordinates (see Fig. 2.1a). It continues moving to the left and is more than 50 m to the left of x 5 0 when we stop recording information after our sixth data point. A graphical representation of this information is presented in Figure 2.1b. Such a plot is called a position time graph. Notice the alternative representations of information that we have used for the motion of the car. Figure 2.1a is a pictorial representation, whereas Figure 2.1b is a graphical representation. Table 2.1 is a tabular representation of the same information. Using an alternative representation is often an excellent strategy for understanding the situation in a given problem. The ultimate goal in many problems is a math- The car moves to the right between positions and. x (m) x (m) a The car moves to the left between positions and. x (m) t b x t (s) Figures from Serway & Jewett Figure 2.1 A car moves back and forth along a straight line. Because we are interested only in the car s translational motion, we can model it as a particle. Several representations of the information about the motion of the car can be used. Table 2.1 is a tabular representation of the information. (a) A pictorial representation of the motion of the car. (b) A graphical representation (position time graph) of the motion of the car.

51 Table 2.1 Position of the Car at Various Times Position t (s) x (m) vs. Time Graphs origin of coordinates (see Fig. 2.1a). It continues moving to the left and is more than 50 m to the left of x 5 0 when we stop recording information after our sixth data point. A graphical representation of this information is presented in Figure 2.1b. Such a plot is called a position time graph. Notice the alternative representations of information that we have used for the motion of the car. Figure 2.1a is a pictorial representation, whereas Figure 2.1b is a graphical representation. Table 2.1 is a tabular representation of the same information. Using an alternative representation is often an excellent strategy for understanding the situation in a given problem. The ultimate goal in many problems is a math- The car moves to the right between positions and. x (m) x (m) a The car moves to the left between positions and. x (m) t b x t (s) Figures from Serway & Jewett Figure 2.1 A car moves back and forth along a straight line. Because we are interested only in the car s translational motion, we can model it as a particle. Several representations of the information about the motion of the car can be used. Table 2.1 is a tabular representation of the information. (a) A pictorial representation of the motion of the car. (b) A graphical representation (position time graph) of the motion of the car.

52 Summary quantities for describing motion: position x, velocity v, (acceleration a), time t position, displacement, and velocity are vector quantities (have signs) distance and speed are scalar quantities (always positive) all of these quantities can be plotted against time these quantities are related by derivatives / antiderivatives (Uncollected) Homework Serway & Jewett, Ch 1, onward from page 14. Problems: 9, 45, 57, 67, 71 Ch 2, onward from page 49. Obj. Q: 1; CQ: Concep. Q: 1; Probs: 1, 3, 7, 11