Mr. Chimenti Room 125 West Branch

Scalar and Vector Values Scalar any value that has magnitude but no direction Examples of scalar quantities Height, distance, mass, volume, density, etc. Vector Any value that has magnitude and direction Vectors are drawn as arrows in the direction of the magnitude The length of the arrow representing the vector is proportional to the magnitude of the vector Examples of vector values Velocity, acceleration, force, weight

Adding and subtracting vectors Vector addition Draw vectors and place them “tip to tail” The “resultant” vector is drawn from the tail of the first vector to the tail of the last vector Vector subtraction Subtraction is done by drawing a vector of the same size but opposite direction as the vector that is being subtracted Web Link

Vector addition Vector a Vector b a b a+b resultant a b a-b resultant

Multiplying and dividing vectors Vectors can also be multiplied or divided by scalar values making them larger or smaller a 2a

Describing and measuring motion Motion Anytime that the distance between 2 objects changes Motion is relative to a reference point (usually an object that is stationary) Distance Measurement of how far one point is from another SI unit=meter (a little more than 39 inches) An olympic pool=50m, football field=91m

US Conversion Steps (Dimensional Analysis) 1. Read the question to figure out what you have/know for information. The question will provide you with information that identifies your starting point and your final destination. Starting point = the number and unit provided by the question Final destination = the units desired after converting 2. Using the information gathered from the question, write your starting point and your final destination. 3. Determine the means in which you will get from your starting point to your final destination (simply find “connections” or conversion factors between your starting and final unit). 4. Create a fraction by placing your starting point over one. 5. Multiply between fractions. 6. Write in the bottom unit of the new fraction. This should be the same as the top unit of the previous fraction. 7. Write one set of “connections” or conversion factors into the fraction. Your bottom unit will guide you. 8. Ask yourself, “Do I have the desired unit (final destination) on the top of the new fraction?” NOYES 9. Cancel any units that are diagonal. (This should leave you with only the units that represent your final destination) 10. Multiply the top of the fractions…multiply the bottom of the fractions…divide the top by the bottom. (Go back to step 5)(Proceed to step 9)

Practice Conversions 1. How many seconds are in 6 minutes? 360 seconds 2. How many centimeters are in 27 inches? centimeters 3. If a truck weighs 15,356 pounds, how many tons is it? tons 4. If you had 10.5 gallons of milk, how many pints would you have? 84 pints 5. Students go to school for 180 days. How many minutes is this equal to? 259,200 minutes

How many seconds are in 6 minutes? 6 minutes  seconds (6 minutes) 1 ( ) seconds minute 360 seconds 60 1 = (6)(60 seconds) (1)(1) = Step 1 – Read the question and determine what information it provides you with (starting point & final destination) Step 2 – Write down your starting point and your final destination 1 minute = 60 seconds Step 3 – Determine how you will get from your starting point to your final destination (list any “connections” or conversion factors) Step 4 – Create a fraction by placing your starting point over one Step 5 – Multiply between fractions Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 7 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 8 – Determine if this top unit is the desired unit (your final destination). In this case the answer is YES, so we move on to step 9 Step 9 – Cancel all diagonal units. Once this is done, your final destination should be the only unit left – in this case seconds Step 10 – Multiply the top of the fractions; multiply the bottom of the fractions; divide the product of the top by the product of the bottom Starting Point Final Destination

How many centimeters are in 27 inches? 27 inches  centimeters (27 inches) 1 ( ) cm inch centimeters = (27)(2.54 cm) (1)(1) = Step 1 – Read the question and determine what information it provides you with (starting point & final destination) Step 2 – Write down your starting point and your final destination 1 inch = 2.54 centimeters Step 3 – Determine how you will get from your starting point to your final destination (list any “connections” or conversion factors) Step 4 – Create a fraction by placing your starting point over one Step 5 – Multiply between fractions Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 7 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 8 – Determine if this top unit is the desired unit (your final destination). In this case the answer is YES, so we move on to step 9 Step 9 – Cancel all diagonal units. Once this is done, your final destination should be the only unit left – in this case centimeters Step 10 – Multiply the top of the fractions; multiply the bottom of the fractions; divide the product of the top by the product of the bottom Starting Point Final Destination

If a truck weighs 15,356 pounds, how many tons is it? 15,356 pounds  tons (15,356 lbs.) 1 ( ) ton lbs tons = (15,356)(1 ton) (1)(2000) = Step 1 – Read the question and determine what information it provides you with (starting point & final destination) Step 2 – Write down your starting point and your final destination 2000 pounds = 1 ton Step 3 – Determine how you will get from your starting point to your final destination (list any “connections” or conversion factors) Step 4 – Create a fraction by placing your starting point over one Step 5 – Multiply between fractions Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 7 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 8 – Determine if this top unit is the desired unit (your final destination). In this case the answer is YES, so we move on to step 9 Step 9 – Cancel all diagonal units. Once this is done, your final destination should be the only unit left – in this case tons Step 10 – Multiply the top of the fractions; multiply the bottom of the fractions; divide the product of the top by the product of the bottom Starting Point Final Destination

If you had 10.5 gallons of milk, how many pints would you have? 10.5 gallons  pints (10.5 gallons) 1 ( ) quarts gallon 84 pints 4 1 = (10.5)(4)(2 pints) (1)(1)(1) = Step 1 – Read the question and determine what information it provides you with (starting point & final destination) Step 2 – Write down your starting point and your final destination 1 gallon = 4 quarts 1 quart = 2 pints Step 3 – Determine how you will get from your starting point to your final destination (list any “connections” or conversion factors) Step 4 – Create a fraction by placing your starting point over one Step 5 – Multiply between fractions Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 7 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 8 – Determine if this top unit is the desired unit (your final destination). In this case the answer is NO, so we move back to step 5 Step 9 – Cancel all diagonal units. Once this is done, your final destination should be the only unit left – in this case pints Step 10 – Multiply the top of the fractions; multiply the bottom of the fractions; divide the product of the top by the product of the bottom Starting PointFinal Destination ( ) pints quart 2 1 Step 5 – Multiply between fractions Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 7 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 8 – Determine if this top unit is the desired unit (your final destination). In this case the answer is YES, so we move on to step 9

Students go to school for 180 days. How many minutes is this equal to? 180 days  minutes (180 days) 1 ( ) hours day 259,200 minutes 24 1 = (180)(24)(60 minutes) (1)(1)(1) = Step 1 – Read the question and determine what information it provides you with (starting point & final destination) Step 2 – Write down your starting point and your final destination 1 day = 24 hours 1 hour = 60 minutes Step 3 – Determine how you will get from your starting point to your final destination (list any “connections” or conversion factors) Step 4 – Create a fraction by placing your starting point over one Step 5 – Multiply between fractions Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 7 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 8 – Determine if this top unit is the desired unit (your final destination). In this case the answer is NO, so we move back to step 5 Step 9 – Cancel all diagonal units. Once this is done, your final destination should be the only unit left – in this case minutes Step 10 – Multiply the top of the fractions; multiply the bottom of the fractions; divide the product of the top by the product of the bottom Starting PointFinal Destination ( ) minutes hour 60 1 Step 5 – Multiply between fractions Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 7 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 8 – Determine if this top unit is the desired unit (your final destination). In this case the answer is YES, so we move on to step 9

Online Tutorials /tutorials/ch1.htm /tutorials/ch1.htm (click on “view tutorial” for dimensional analysis) /practice/index.html /practice/index.html (click on examples under dimensional analysis on the left side of the page) Interactive Quiz

The ladder method Metric units that have common base units can be converted by moving a decimal point to the left or right This method is called the ladder method

Calculating Speed (Scalar values) Speed The distance that an object travels within a period of time Speed=distance÷time Average speed The total distance traveled dived by the total time Speed changes throughout the trip Ave. speed=total distance÷ total time Instantaneous speed Rate of motion at a certain point in time

Velocity (vector value) Velocity A measure of the speed and direction of motion a vector value (magnitude and direction) Vectors are drawn as arrows

Graphing motion Plotting distance (y- axis) over time (x-axis) is one way to display motion The slope of a distance vs. time graph gives you the instantaneous velocity

Acceleration (vector value) Acceleration-rate at which velocity changes 3 ways: speed up, slow down or change direction Acceleration always occurs in the direction of a force applied to an object Acceleration=(final velocity-initial velocity)÷time The slope of a velocity (y) vs. time (x) graph will give you the acceleration of an object A curved line on a distance vs. time graph tells you that acceleration is occuring

Acceleration (vector value)

Forces (vector value) Force-any push or pull on an object Measured in Newtons (N) 1N=1kgm/s 2 2 or more forces can be added together forming a “net force”

Forces (continued) Unbalanced forces Combination of forces which cause an object to accelerate One or more forces overpower the other force or forces Balanced forces Combination of forces which do not cause an object to accelerate

Friction Friction-forces exerted by 2 objects on one another when they rub against one another Frictional forces always oppose motion Frictional force converts motion (kinetic energy) of an object into thermal energy (heat)

4 types of friction Static friction Force opposing the motion of an object that is not in motion Sliding friction Force opposing the motion of an object that is sliding over the surface of another Rolling friction Force opposing the motion of an object that is rolling over top of another Fluid friction Force opposing the motion of an object and the fluid that it is moving through

Gravity Gravity-force of attraction which pulls objects toward one another All objects in the universe are attracted to one another Larger objects pull harder than small one (increase mass, increase gravity) The closer two objects are the greater the gravity is between them (decrease distance, increase gravity) Mass=the amount of matter in an object Weight=the magnitude of the force of gravity on an object (increase mass, increase weight) Mass is commonly calculated by measuring the force of gravity acting on an object

Gravity and Motion Free-fall=condition in which the only force on an object is gravity Acceleration due to gravity is 9.8m/s 2 Free fall occurs in the absence of air resistance All objects free fall at the same rate Air resistance Def.=Fluid friction between an object and air A reason why some objects fall slower than others Terminal velocity The greatest velocity that an object in free fall can reach (air resistance=objects weight)

Projectile motion Describes the motion of any object which is thrown Projectile motion occurs in 2 or 3 dimensions

Newton’s laws of motion 1 st law of motion An object at rest will stay at rest, an object in motion will stay in motion unless acted on by an unbalanced force. Aka the “law of inertia” Inertia=tendancy of an object in motion to resist a change in its motion The greater the mass of an object the more inertia it possesses

Newton’s laws of motion 2 nd law of motion An object will accelerate in the direction of an unbalanced force Acceleration=net force÷mass

Newtons laws of motion 3 rd law of motion If one object exerta s force on another object the other object exerts a force of equal size in the opposite direction on the first object Aka “action-reaction” Action-reaction forces do not always cancel out each others motion due to differences in mass

momentum A characteristic of all moving objects Describes how difficult it is to stop an objects motion Momentum=mass x velocity Law of conservation of momentum The sum of the momentum of objects in a collision do not change

collisions Elastic collsions=objects bounce off of one another after a collision Inelastic collisions=objects stick together after they collide As long as objects retain their shape momentum in conserved