Chapter 1: Measurements & Units Chapter 2: 1D Kinematics Thursday January 6th The International system of units (SI) Prefixes for SI units Orders of magnitude Changing units Length, time and mass standards Motion in a straight line (1D Kinematics) Average velocity and average speed Instantaneous velocity and speed Acceleration Reading: pages 1 – 22 in the text book (Chs. 1 & 2)

Physics 2048: Reminders First LON-CAPA assignment due Monday First LON-CAPA assignment due Monday First assignment mainly review (not all covered in lecture) First assignment mainly review (not all covered in lecture) Very strict deadline of 11:59:59 pm on due date Very strict deadline of 11:59:59 pm on due date First Mini-Exam next Thursday (Jan. 13 th ) First Mini-Exam next Thursday (Jan. 13 th ) You must attend your first lab next week (M/W) You must attend your first lab next week (M/W) Refer to Appendix A in Text Book Trigonometry, Law of cosines, etc….

The International System of Units Système International (SI) d'Unités in French a.k.a. metric or SI units Scientists measure quantities through comparisons with standards. Every measured quantity has an associated unit. The important thing is to define sensible and practical "units" and "standards" that scientists everywhere can agree upon. (e.g. Rocket Scientists)

The International System of Units Système International (SI) d'Unités in French a.k.a. metric or SI units Even though there exist an essentially infinite number of different physical quantities, we need no more than seven base units/quantities from which all others can be derived. In 1971, the 14th General Conference on Weights and Measures picked these seven base quantities for the SI, or metric system. In Mechanics, we really only need three of these base units (see table) In Thermodynamics, we need two more Temperature in kelvin (K) Quantity in moles (mol)

Prefixes for SI Units m = 3.56 × 10 9 m s = 4.92 × s On LON-CAPA = 4.92*10^-7 s On your calculator (also LON-CAPA): 4.92 × = 4.92 E-7 or Prefixes (also works in LON-CAPA): 5 × 10 9 watts = 5 gigawatts = 1 GW 2 × s = 2 nanoseconds = 2 ns Scientific notation:

Orders of magnitude

Changing units Chain-link conversion - an example: 1 minute = 60 seconds Note: this does not imply 60 = 1, or 1/60 = 1!

Conversion Factors Etc., etc., etc……. Resources at your fingertips…

Which of the following have been used as the standard for the unit of length corresponding to 1 meter? a) One ten millionth of the distance from the North pole to the equator. b) The distance between two fine lines engraved near the ends of a platinum-iridium bar. c) wavelengths of a particular orange-red light emitted by atoms of krypton-86 ( 86 Kr). d) The length of the path traveled by light in a vacuum during a time interval of 1/ of a second. Quiz #1

Length 1 m = distance from N. pole to equator ten-million 1792: French established a new system of weights and measures Then, in the 1870s: 1 m = distance between fine lines on Pt-Ir bar Accurate copies sent around the world Then, in 1960: 1 m = × wavelength 86 Kr (orange) 1983 until now (strict definition): 1 m = distance light travels in 1/( ) sec

Time Length of the day Period of vibration of a quartz crystal Now we use atomic clocksNow we use atomic clocks Some standards used through the ages: 1 second equivalent to oscillations of the light emitted by a cesium-133 atom ( 133 Cs) at a specified wavelength (adopted 1967) United States Naval Observatory

Mass A second mass standard: The 12 C atom has been assigned a mass of 12 atomic mass units (u)The 12 C atom has been assigned a mass of 12 atomic mass units (u) 1 u = × Kg The masses of all other atoms are determined relative to 12 CThe masses of all other atoms are determined relative to 12 C Note: we measure "mass" in kilograms. Weight is something completely different, which we measure in Newtons (  kg  m/s 2 ) Kilogram standard is a Pt-Ir cylinder in Paris Accurate copies have been sent around the world; the US version is housed in a vault at NIST

Summary

Motion in one-dimension We will define the position of an object using the variable x, which measures the position of the object relative to some reference point (origin) along a straight line ( x -axis). Positive direction Negative direction

Motion in one-dimension We will define the position of an object using the variable x, which measures the position of the object relative to some reference point (origin) along a straight line ( x -axis). Positive direction Negative direction

Motion in one-dimension We will define the position of an object using the variable x, which measures the position of the object relative to some reference point (origin) along a straight line ( x -axis). In general, x will depend on time t. We shall measure x in meters, and t in seconds, i.e. SI units. Although we will only consider one- dimensional motion here, we should not forget that x is really a vector. Thus, motion in the + x and - x directions corresponds to motion in opposite directions. Positive direction Negative direction

Graphing x versus t x(t)x(t)

Displacement Displacement  x:  x = x 2  x 1 final  initial position Like x,  x is a vector quantity Like x,  x is a vector quantity Its magnitude represents a distance Its magnitude represents a distance The sign of  x specifies direction The sign of  x specifies direction x2x2 x1x1

Average velocity  x = 4 m  (  10 m) = 14 m  t = 5 s  0 = 5 s

Average velocity and speed Like displacement, v avg is a vectorLike displacement, v avg is a vector s avg is not a vector - it lacks an algebraic sign s avg is not a vector - it lacks an algebraic sign How do v avg and s avg differ?How do v avg and s avg differ? Average speed s avg :

Instantaneous velocity and speed v1v1 v2v2 v3v3 v 3 > v 1 > v 2 Instantaneous speed = magnitude of v Instantaneous speed = magnitude of v

Acceleration An object is accelerating if its velocity is changingAn object is accelerating if its velocity is changing Average acceleration a avg : Instantaneous acceleration a : This is the second derivative of the x vs. t graphThis is the second derivative of the x vs. t graph Like x and v, acceleration is a vectorLike x and v, acceleration is a vector Note: direction of a need not be the same as vNote: direction of a need not be the same as v

Accelerating a v Decelerating a v x(t)x(t)

Accelerating a v Decelerating a v x(t)x(t) v(t)v(t) v 3 > v 1 > v 2

Accelerating a v Decelerating a v v(t)v(t)a(t)a(t)

Summarizing Average velocity: Displacement:  x = x 2  x 1 Instantaneous velocity: Average speed: Instantaneous speed:magnitude of v

Summarizing Average acceleration: Instantaneous acceleration: In addition: SI units for a are m/s 2 or m.s  2 (ft/min 2 also works)

The sensation of acceleration You will soon learn that, in order to accelerate an object, one must exert a net force on that object. Thus, when you accelerate, you experience stresses associated with the net force applied to your body. Therefore, your body is an accelerometer. When you travel at a constant velocity, be it on a bicycle at 10 ms -1, or a supersonic aircraft at 1500 mph, you are not accelerating. Therefore, you do not feel the sensation of any net force, i.e. your body is not a speedometer. Acceleration is often expressed in terms of g units, where g (= 9.8 ms -1 ) is the magnitude of the acceleration of an object falling under gravity close to the earth's surface.

Constant acceleration: a special case For non-calculus derivations, see section 2-4 in text book To evaluate the constant of integration C, we let v = v o at time t = 0, i.e. v o represents the initial velocity.To evaluate the constant of integration C, we let v = v o at time t = 0, i.e. v o represents the initial velocity. Taking the derivative of Eq. 2-7 ( v o and a are constants), we recover:Taking the derivative of Eq. 2-7 ( v o and a are constants), we recover:

Further integration Note - in general, v depends on t. However, we can substitute v from Eq. 2-17:Note - in general, v depends on t. However, we can substitute v from Eq. 2-17: To evaluate the constant of integration C', we let x = x o at time t = 0, i.e. x o represents the initial position.To evaluate the constant of integration C', we let x = x o at time t = 0, i.e. x o represents the initial position.

Equations of motion for constant acceleration Equations 2-11 and 2-15 contain 5 quantities: a, t, v, v o and the displacement x - x o.Equations 2-11 and 2-15 contain 5 quantities: a, t, v, v o and the displacement x - x o. Both equations contain a, t and v o.Both equations contain a, t and v o. One can easily eliminate either a, t or v o by solving Eqs and 2-15 simultaneously.One can easily eliminate either a, t or v o by solving Eqs and 2-15 simultaneously.

Free fall acceleration If one eliminates the effects of air resistance, one finds that all objects accelerate downwards at the same constant rate, regardless of their mass (Galileo).If one eliminates the effects of air resistance, one finds that all objects accelerate downwards at the same constant rate, regardless of their mass (Galileo).Galileo That rate is called the free-fall acceleration g.That rate is called the free-fall acceleration g. The value of g varies slightly with latitude, but for this course g is taken to be 9.8 ms -2 at the earth's surface.The value of g varies slightly with latitude, but for this course g is taken to be 9.8 ms -2 at the earth's surface. Thus, the equations of motion in table 2-1 apply to free- fall near the earth's surface.Thus, the equations of motion in table 2-1 apply to free- fall near the earth's surface. HRW substitute the coordinate y for x in problems involving free-fall.HRW substitute the coordinate y for x in problems involving free-fall. It is customary to consider y as increasing in the upward direction. Therefore, the acceleration a due to gravity is in the negative y direction, i.e. a = -g = -9.8 ms -2.It is customary to consider y as increasing in the upward direction. Therefore, the acceleration a due to gravity is in the negative y direction, i.e. a = -g = -9.8 ms -2.