Math Review/ Physical Properties

Old Business Two Graduate Assistants Kevin Blue Justin Darrow helping out Check your BSU MET-L

Proportional / Inversely Proportional Consider the following equation v = d / t (velocity = distance / time) d = v x t (equivalent relation) Two quantities in an equation are Proportional if the ratio between them is constant. (x  y) Two quantities are Inversely Proportional if their product is constant. (x  1/y)

Quick Keys to Recognizing Variables raised to different powers will not be proportional or inversely proportional. Numerator to Numerator on different sides of equal sign can be proportional. Numerator to Denominator on different sides of equal sign can be inversely proportional. Factors on one side of equality statement will be inversely proportional. (if the only two factors)

Exponents Anything to the “zeroeth” power equals 1. A negative exponent equals 1 divided by positive power of the number. n -2 = 1 / n 2 Remember your power of 10 “tricks” Multiplying quantities with the same base is the same as adding the exponents. Dividing quantities with the same base is the same as subtracting the exponents.

Cartesian Coordinates/Functions Graphing can show relationship between two quantities. x is horizontal axis; y is vertical x is the independent variable (it changes by itself within a permissible range); y is dependent on the value of x--it changes as a function of x.

Graphical Representation of a Sound Wave Representation Typically, shows the measure of sound pressure (air pressure) as a function of time.

Units of Measurement Système International (SI) Meters, Kilograms, Seconds When solving problems, you must always specify the unit of measurement for any value you arrive at. It is extremely helpful (and hence highly recommended) to specify the unit of measurement for all values in an equation.

Motion distance = speed x time speed = distance / time time = distance / speed velocity = speed and specified direction constant speed and average speed

Mass Mass is not weight Weight = mass x force_of_gravity Mass measured in kg Weight is measured in society in kg or lbs. Scientifically, weight is measured in Newtons. 1 kg of mass accelerated 1m/s 2 = 1Newton

Newton’s Second Law The acceleration of an object is equal to the net force F divided by its mass m.

Acceleration Change in speed Earth’s gravity has an acceleration of 9.8 m/s 2.

Force Force is measured in Newtons. (the actual unit, or unit ratio is messy.)

Pressure Newton’s second law doesn’t care if one force is acting at a single point, or if many forces are acting at many points. Center of gravity (entire force acting at one point) Pressure is the distribution of force over an area Perpindicular

Pressure (2) Force measure in Newtons; area measured in meters 2. Pressure measured in Newtons/meter 2, or often in Pascals (1 Pa = 1 N/m 2 ).

Work Work (W ) = force times distance Work is measured in newton-meters, or joules (J). Object in free fall: W = mgh Time doesn’t matter.

Energy In order to do work, energy must be expended. Work is the transfer of energy Energy comes in several forms, but in this class we’re mostly concerned with kinetic energy (KE) and potential energy (PE).

Energy (2) PE is the amount of work that an object can do. PE = mgh (object raised to height) PE = 1/2(Ky 2 ) (spring stretched by amount y; K = stiffness) PE = (2T/L)y 2 (string of tension T, length L, displaced by y) KE is the energy of motion. KE = 1/2(mv 2 ) PE and KE for a given object and situation are equal. How much velocity an object acquires while doing work can be shown by solving for v

Power Work doesn’t specify time. Power is the measure of work divided by time, expressed in watts (1 watt = 1 joule/second)

Homework Assignment 1 handout Chapter 1 exercises, numbers 2, 4, 6, 8, 10, 12(a) and 12(b). (pp. 19 and 20) Important: Start by writing out the formula you are using to solve the problem. Make sure that you are using the correct units, especially for relational units such as Newtons, Joules, and Watts.