Mrs. Johnson's Science
UNITSMassMetric:GramsgKilogramkgEnglish:OunceozPoundlbTontonVolumeMetric:MillilitermlCubic centimeterccLiterLEnglish:TeaspoontTablespoonTCupcPintptFluid ouncefl ozGallongalFoot acreft acreLengthMetric:MillimetermmCentimetercmMetermKilometerkmEnglishinchinFootftYardydMilemiForceMetric:NewtonN PressureMetricPascalPEquivalent UnitsWithin the metric systemMetric PrefixKilogram = 1,000 gramkilo ___________ = 1,000 _____________decagram = 10 gramsdeca __________ = 10 ________________10 decigrams = 1 gram10 deci _______ = _1_________________100 centigrams = gram100 centi ____ = _1_________________1,000 milligrams = gram1,000 milli ___ = _1_________________1,000,000 grams = 1 megagram1 mega _______ = 1,000,000 _______1 cubic centimeter = 1 milliliter1 metric ton = 1,000 kilograms Use anything to fill in the blank of the metric prefix as long1 Newton = 1 kg x m/s2as both blanks are the same thing!1 Pascal = 1 N x mExample:Within the English system1 kilobanana = 1,000 bananas16 ounces = 1 pound2,000 pounds = 1 short ton12 inches = 1 foot3 feet = 1 yard1 mile = 1,760 yards 1 tablespoon = 3 teaspoons?2 tablespoon = 1 fluid ounce 16 fluid ounces = 1 pint2 pints = 1quart4 quarts = 1 gallonConverting Between Metric and English1 ounce = 28.35 grams1 kilogram = 2.205 pounds1 inch = 2.54 centimeters?1 foot = 0.305 meter?0.62 miles = 1 kilometer1 fluid ounce = 29.6 milliliters1 pint = .473 liter1 gallon = 3.8 liters1 liter = 1.06 quartsHow to Convert from one unit to Another(example: how many seconds are in 10 days?)Draw a line to make a fraction and place a 1 on the bottom.__________ 1Place the value you know (with the unit that goes with it) on the top of the fraction.10 days 1Place a multiplication sign next to the fraction.10 days x 1Draw a line for a new fraction to the right of the multiplication sign.10 days x __________ 1place the unit you want to get rid of on the side of the fraction that will cause it to cancel. If the unit is on the top of the fraction, place the same unit on the bottom of the next fraction.10 days x ____________ 1 daysFind a conversion factor that uses the unit you are trying to get rid of and either gives you the unit you want or gets you a step closer to the unit you want.REMEMBER - A conversion factor is just a fraction that equals 1. In order for the fraction to equal 1 the top of the fraction and the bottom of the fraction must have the same value.1 day = 24 hours so I can make a conversion factor of 1 day = 1because the fraction has a value 1. 24 hoursPlace the unit you are changing from on the bottom of the fraction.10 days x ___________daysPlace the unit you are changing to on the top of the fraction.10 days x ___hoursdaysNotice the numbers in the conversion factor. The numbers should be placed in the equation next to the same unit. The conversion factor 1 day = 24 hours10 days x 24_hours1 daysYou can either multiply another conversion factor or finish by cancelling and calculating.----- Finish & calculate ----Cross out any unit that is both on the top and the bottom of fractions. Multiply both numbers and units across the top. Do the same for the bottom. Simplify the fraction10 days x _24_hours = 10 x 24 hours = 240 hours1 days 1---- Multiply another conversion factor ----Repeat the procedure with another conversion unit. Keep multiplying conversion factors until the result has the unit you want.10 days x _24_hours Conversion factors: 1 hour = 60 min1 days 1 min = 60 sec10 days x _24_hrs x 60 min x __60_sec = 10 x 24 x 60 x 60 sec = 1 days 1 hour 1 min 1 x 1 x 1 864,000 secUNIT CONVERSION EXAMPLESMETRICHow many kilometers are in 100 millimeters?Conversion factors: 1,000 millimeters = 1 meter 1,000 meters = 1 kilometer100 mm x 1 m___ x __1_km = 100 x km = 100 km = 1 km 1 1,000 mm 1,000 m 1,000 x 1,000 1,000,000 10,000 ENGLISH TO METRICHow many centimeters are in 10 yards?Conversion factors: 1 foot = 12 inches 1 inch = 2.54 centimeters10 ft x 12 in x __2.54 cm = 10 x 12 x 2.54 cm = 204.8 cm 1 1 ft 1 in 1UNITS ON BOTH THE TOP AND BOTTOM OF THE FRACTIONDensity is given as 7.6 kilograms per gallon. Change this to a density with units of grams per milliliter.Conversion factors: 1 kg = 1,000 g1 gal = 3.8 L1,000 ml = 1 L7.6 kg x 1,000 g x _ 1 gal x 1 L = 7.6 x 1,000 g = 7,600 g = 2 g 1 gal1 kg 3.8 L 1,000 ml 3.8 x 1,000 ml 3,800 ml mlMath FormulasVolume of a box = length x width x height V = l x w x h Volume measured by displacement = final volume – initial volume Mass found by displaced water: displaced water x 1 g/ml = mass in gramsDensity = mass D = m/v VolumeConcentration = mass in soluteC = m/v Volume of solventAverage speed =change in distance S = ?d/?tChange in timeAverage acceleration = change in velocitya = ?v/?t Change in timeNet Force = the sum of all forces Force = mass x acceleration F = maWeight = mass x acceleration due to gravityWt = m x gMomentum = mass x velocityP = m x vPressure = ForceP = F/a AreaDegrees Fahrenheit = (9/5 x degrees Celsius) + 32?F = (9/5 x ?C) + 32 Multiply degrees Celsius by 9. Divide by 5. Add 32. The answer is FahrenheitDegrees Celsius = (degrees Fahrenheit – 32) x 5/9?C = (?F - 32) x 5/9 Take the degrees Fahrenheit and subtract 32. Multiply the answer by 5. Divide by 9. The answer is in CelsiusAtomic mass unit = mass in one protonAtomic number = number of protons in an atomAtomic mass = number of protons plus the number of neutronsUNITS for formulasSolid volume: (any length measurement)3 cm3 m3 in3 yd3 mi3Density: any measurement of mass g/mL kg/L lbs/gallon (and so on) Any measurement of volumeConcentration: any measurement of mass usually g/mL Any measurement of volume but it can be anything! (see density units)Speed: any measurement of distance m/s mi/hr in/year (and so on) Any measurement of timeAcceleration: any measurement of distance Any measurement of time x any measure of timem/s2 mi/hr2 in/year 2 (and so on)Force = Newtons (N) A Newton = kg x mTHESE ARE THE ONLY UNITS!!!!! s2When calculating force you must use kg for mass and m/s2 for acceleration.Weight: Newtons (N) A Newton = kg x mTHESE ARE THE ONLY UNITS!!!!! s2 When calculating weight you MUST use kg for mass. Gravity is always given in m/s2Momentum: kg x mFor calculations with momentum, the ONLY units used sare kg, m, and sPressure: Newton or kilogram This unit is called a Pascal Meter meter x s2FYI English unit for pressure is psi or “pounds per square inch. The units are lb in2 Name: ___________________________________(p. 1 out of 2)Math Set #1 Units Write the entire word “volume” or “length” or “mass” to the left of each unit.Write the abbreviation for each unit on the line to the right of the unit.______________________________ Kilogram_____________________________________________ Centimeter_____________________________________________ Teaspoon_____________________________________________ Ounce_____________________________________________ Mile_____________________________________________ Foot acre_____________________________________________ Milliliter_____________________________________________ Cubic centimeter_____________________________________________ Inch_____________________________________________ Tablespoon_____________________________________________ Cup_____________________________________________ Meter_____________________________________________ Pint_____________________________________________ Gram_____________________________________________ Gallon_____________________________________________ Pound_____________________________________________ Millimeter_____________________________________________ Kilometer_____________________________________________ Liter_____________________________________________ Foot_____________________________________________ Yard_____________________________________________ Ton_____________________________________________ Fluid ounce_______________Name: ___________________________________(p. 2 out of 2)Math Set #1 Units Fill in the blank with a number.10 decigrams = ________________ grams1,000 milliliters = _______________ liters1 kilometer = _______________ meters1 megabanana = ______________ bananasCalculationsThe formula for converting Fahrenheit to Celsius is C = 5/9 (F – 32)If you had a Fahrenheit Temperature reading how would you convert it to Celsius?If you had a Celsius Temperature reading how would you convert it to Fahrenheit?Fill in the following TableWhat temperature was measured?DegreesFahrenheitDegreesCelsiusDoes it feel hot, warm, cool, or cold?Air Outside the House50Air Inside the House5Water in a Pool30Water in a Pool35Coca Cola68The Human Body40Name: ___________________________________ (p.1 of 4)Math Sheet set#2 MeasurementIf you put a liquid in a glass container it usually curves at the edges. This curvature is called the meniscus. To get an accurate measurement, you measure the level at the horizontal center. This is the part of the meniscus that is at the very center. With meniscus that curve up at the edges you read the “bottom of the meniscus.”4051935104775188023510477525400635 Remember that the only way to read a meniscus properly is to have your eyes at the level of the top of the liquid. Read the bottom of the meniscus. DIRECTIONS: Give the volume in the following graduated cylinders Make sure you include mL in your answers.A. _____________ B. ____________ C. ____________ D. _____________ E. _____________Name: ___________________________________ (p. 2 of 4)Math Sheet Week#2 Measurement508635152400 Explain what this diagram shows. USE COMPLETE SENTENCES.BACMeasure the following lines. Give the length in both inches and centimeters.A. _________________ cmB. ___________________ cmC. _________________ cmA. ________________ inB. ___________________ inC. _________________ in(p.3 of 4)Name: ___________________________________ TRY THIS WITHOUT LOOKING! then check and correct)Math Set #2Write the entire word “volume” or “length” or “mass” to the left of each unit.Write the abbreviation for each unit on the line to the right of the unit.______________________________ Kilogram_____________________________________________ Teaspoon_____________________________________________ Ounce_____________________________________________ Mile_____________________________________________ Foot acre_____________________________________________ Milliliter_____________________________________________ Cubic centimeter_____________________________________________ Inch_____________________________________________ Tablespoon_____________________________________________ Cup_____________________________________________ Meter_____________________________________________ Pint_____________________________________________ Gram_____________________________________________ Gallon_____________________________________________ Pound_____________________________________________ Kilometer_____________________________________________ Liter_____________________________________________ Foot_____________________________________________ Yard_____________________________________________ Ton_____________________________________________ Fluid ounce_______________(p.4 of 4)Name: ___________________________________ Math Set #2Remember – a conversion factor is a fraction that equals 1. You can multiply anything by 1 and not change the value, even though the form looks different.22 x 1 = 1/1 = 475 x 1 =475/475 =a banana x 1 =a banana/a banana =Circle each item that can be used as a conversion factor72 48___300a banana 724 x 1212 inches1,000 liter10 golf balls1 foot1 kiloliter 1 basketballRewrite these equivalents so that they are in fraction form and set them = 1Example: 12 inches = 1 foot ---- 12 inches = 1 1 foot1 decagram = 10 grams3 feet = 1 yard1 foot – 0.305 meter1 cubic millimeter = 1 milliliter2 pints = 1 quart1 kilogram = 2.205 pounds16 ounces = 1 pound1 tablespoon = 3 teaspoons1,000,000 grams = 1 megagramName: ___________________________________ (p. 1 of 3)Math Sheet Week#3 VolumeThree types of volume can be measured. That of a solid, liquid and gas.How is the volume of a rectangular solid measured? What are the units?How is the volume of a liquid measured? What are the units?How is the volume of a gas measured? What are the units?How is the volume of an irregular solid measured? What are the units?Give the volume for the following irregularly shaped solids. Write the volume underneath each pair of graduated cylinders.2908935414655-177165136525Name: ___________________________________ (p.2 of 3)Math Set Week# 3 VolumeThe volume of a box can be calculated by the formula Volume = length x width x height (V = L x W x H)Set up these problems like the example and be sure to include all units in order to get full credit.Example: What is the volume of this box?Answer: L = 2 cmV = L x W x HW = 5 cmvolume = 2 cm x 5 cm x 4 cm H = 4 cmvolume = 40 cm3What is the volume of this box?-29146588265222313530480What is the volume of this box?What is the volume of this box? 51435301625Name: ___________________________________(p.3 of 3)Math Set # 3 conversion factorsWrite the conversion factor that would be used to change the units. Make sure that the fraction has the correct unit on both the top and the bottom.Example: change from mm to mmm is the unit you want to change, so it goes on the bottom of the fraction.m is the unit you want to end up with, so it goes on the top of the fraction.1,000 mm = 1 m is the equality that has both units and the 1,000 is next to mm. So, the conversion factor would be 1 m_____1,000 mmconversion factor used to convert from pounds to ouncesconversion factor used to convert from milligrams to gramconversion factor used to convert from inches to centimetersconversion factor used to convert from miles to yardscconversion factor used to convert from dollars to penniesconversion factor used to convert from liters to quartsName: ___________________________________(p. 1 of 4)Math Set #4 single step conversionsUse the procedure in your notebook to perform the following conversions. Include all steps in order to get credit. ANSWERS THAT DO NOT SHOW WORK ARE WRONG. ANSWERS WITHOUT UNITS ARE WRONG.Example: How many meters are in 6 kilometers?Answer:6 kilometers x 1,000 meters = 6,000 kilometers1 kilometer372 inches makes how many feet?How many milligrams are in 4.2 grams?208 fluid ounces can make how many pints?What is the weight of a 2 ton truck in pounds?114 centimeters is equal to how many meters?How many milliliters are in 732 cubic centimeters?Name: ___________________________________ (p. 2 of 4)Math Set #4 DensityWould the following substances sink or float when placed in water?Write the word “sink” or “float” on the line next to each item.______________________ gasoline (0.7 g/cm3)______________________ gold (19.3 g/cm3)______________________ aluminum (2.7 g/cm3)______________________ ice (water) (0.92 g/cm3)______________________ wood (oak) (0.85 g/cm3)If the following liquids were gently added to a graduated cylinder they would make layers, one on top of the other. Use the density of each substance to determine the order of the layers. Draw the graduated cylinder with the layers and label each layer.Corn oil (0.93 g/cm3)Alcohol (0.80 g/cm3)Glycerin (1.26 g/cm3)Corn syrup (1.38 g/cm3)Water (1.00 g/cm3)Name: ___________________________________ (p. 3 of 4)Math Set #4 DensityThe density of a solution can be calculated by using the equation Density = mass (D = m/v) volumeSet up these problems like the example and be sure to include all units in order to get full credit.Example: What is the density of an object that weighs 40 grams and takes up 100 mL of space?Answer: D = ?D = m/vm = 40 gdensity = 40 g = 0.4 g v = 100 ml 100 ml mlDensity ProblemsA solid block has a volume of 1,000 ml and a mass of 960 grams. What is the density? Will it sink or float?An sample of oil has a volume of 500 ml and a mass of 650 grams. What is the density? Will it sink or float?A piece of iron has a volume of 2500 ml and a mass of 20,000 grams. What is it’s density? Will it sink or float?Name: ___________________________________ (p.4 of 4)Math Set #4 Mass vs. WeightWrite the word “mass” next to the items that describe mass. Write the word “weight” next to the items that describe weight._____________________________ never changes_____________________________ changes with the size of the both objects (the sun is larger than the earth)_____________________________ is the same on the earth and on the moon_____________________________ is measured in grams and kilograms_____________________________ is measured in Newtons_____________________________ is measured using a spring scale_____________________________ is measured using a balanceOn earth, a 100 gram mass has a weight of approximately 1 Newton. If you know an objects mass you can find the weight using a unit conversion.Weight (in Newtons) = mass (in grams) x 1 Newton 1 100 gA man with places boots that have a mass of 850 grams on a spring scale in order to measure their weight. What reading does he get?A car has a mass of 1,362,000 grams. What is its weight?How much does a 9 kg dog weigh?Name: ___________________________________(p.1 of 2)Math Set#5 converting between systemsUse the procedure in your notebook to perform the following conversions. Include all steps in order to get credit. ANSWERS THAT DO NOT SHOW WORK ARE WRONG. ANSWERS WITHOUT UNITS ARE WRONG.Example: How many millimeters are in 6 kilometers?Answer: 6 kilometers x 1,000 meters x 1,000 millimeters= 6,000,000 kilometers 1 kilometer 1 meter74 cm = ____________________ in25 ml = ____________________ tsp50 kg = ____________________ lbs160 km = ____________________ mi3.6 L = ____________________ gal500 g = ____________________ ozName: ___________________________________(p.2 of 2)-520064177165Math Set #5 Change of StateName: ___________________________________(p.1 of 3)Math Set#6 multiple step conversionsUse the procedure in your notebook to perform the following conversions. Include all steps in order to get credit. ANSWERS THAT DO NOT SHOW WORK ARE WRONG. ANSWERS WITHOUT UNITS ARE WRONG.Example: How many millimeters are in 6 kilometers?Answer: 6 kilometers x 1,000 meters x 1,000 millimeters= 6,000,000 millimeters 1 kilometer 1 meterA man walked 2 miles. A woman walked 63,360 inches. Which one walked farther?How many minutes are in the month of December?How many gallons can be created from 1,152 fluid ounces?How many centigrams are in 3.68 kilograms?8,900 mm equals how many decameters?3 megaliters can be divided into how many deciliters?Name: ___________________________________(p.2 of 3)Math Set#6 multiple step conversionsUse the procedure in your notebook to perform the following conversions. Include all steps in order to get credit. ANSWERS THAT DO NOT SHOW WORK ARE WRONG. ANSWERS WITHOUT UNITS ARE WRONG.Here are some equivalents. Use them to answer the problems.1 chortle = 10 yucks5 giggles = 1 chuckle1 yuck = 4 smirks2 chuckles = 3 hoots3 smirks = 25 giggles1 hoot = 9 guffaws10 giggles are equal to how many hoots?Jennifer has 3 smirks. Joseph has 2 chuckles. Which one has more chuckles?Mary wanted to trade 200 giggles for yucks How many yucks can she get?Convert 10 chuckles into guffaws.How many chortles would you have to give in order to get at least 1,000 giggles?CHALLENGE: Diane has 1 chortle and 3 hoots. John has 10 giggles and 4 yucks. If everything was traded for guffaws, which person would have more?Name: ___________________________________(p.3 of 3)Math Set #6 Boyle’s Law and Charles’ LawBoyle’s Law (fill in the blank)Boyles law applies only to gases when the ______________________________ and the______________________________ stays the same. In these circumstances, Boyle’s law states that the gas ______________________________ is “inversely related” to the ______________________________. “Inversely related” means that when one factor is increased, the other factor is ____________________ by the same amount.A 5 gram mass of air is being held at a constant temperature. You increase the pressure by 20%. How is the volume changed? A 20 gram mass of air is being held at a constant temperature. You increase the volume by 50%. How is the pressure changed? Charles Law (fill in the blank)Charles’ law applies only to gases when the ______________________________ and the______________________________ stays the same. In these circumstances, Charles’ law states that the gas ______________________________ is “directly related” to the ______________________________. “Directly related” means that when one factor is increased, the other factor is ____________________ by the same amount.A 5 gram mass of air is being held at a constant pressure. You increase the temperature by 10%. How is the volume changed? A 20 gram mass of air is being held at a constant pressure. You decrease the volume by 50%. How is the temperature changed? Name: ___________________________________(p.1 of 3)Math Set#7 converting top and bottom unitsUse the procedure in your notebook to perform the following conversions. Include all steps in order to get credit. ANSWERS THAT DO NOT SHOW WORK ARE WRONG. ANSWERS WITHOUT UNITS ARE WRONG.Example: A man is walking 7 miles per hour. How many feet can is he walking every minute?Answer: 7 miles x 1 hour x 1,760 yards x 3 feet = 3,690 feet = 616 feet hour 60 min 1 mile 1 yard 60 min minA ball has a density of 50 centigrams per milliliter. What is the density in grams per liter?A car travels at a speed of 100 meters per minute. What is this speed in kilometers per hour?The density of a liquid is measured to be 20 ounce/quart. What is the density in pounds/gallon?A spider is traveling at 30 feet/sec. How many miles/hour is the spider moving?Name: ___________________________________(p.2 of 3)Math Set #7 Average SpeedAverage Speed = Distance S = d/t TimeYou can rearrange the equation to find time: time = distance t = d/S SpeedYou can rearrange the equation to find distance: distance = speed x time d = s x tExample: How much time would it take for the sound of thunder to travel 2,310 meters if sound travels at the speed of 330 m/sec?S = 330 m/sect = d/Sd = 1,500 mt = 2,310m = 7 sect = ? 330 m/secFOR FULL CREDIT WRITE OUT ALL STEPS AND GIVE ALL UNITSWhat is the average speed of a car that traveled 300.0 miles in 5.5 hours?How much time would it take for an airplane to reach its destination if it traveled at an average speed of 790 kilometers/hour for a distance of 4.700 kilometers?3. A snail can move approximately 0.30 meters per minute. How many meters can the snail cover in 15 minutes?Name: ___________________________________(p.3 of 3)Math Set #7 Average SpeedFOR FULL CREDIT WRITE OUT ALL STEPS AND GIVE ALL UNITS How long would it take you to swim across a lake that is 900 meters across if you swim at 1.5 m/sec?How far will you travel if you run for 10 minutes at 2 m/sec?Suppose you are walking home after school. The distance from school to your home is five kilometers. On foot, you can get home in 25 minutes. However, if you rode a bicycle, you could get home in 10 minutes.What is your average speed while walking?What is your average speed while bicycling?how much faster do you travel on your bicycle?Name: ___________________________________(p.1 of 5) Math Set #8 Average Acceleration Acceleration is how fast an object’s velocity changesAverage acceleration = change in velocityA = final velocity – initial velocityTimetimeA = ? VA = Vf - Vi t tExample: A car increases its velocity from 0 m/s to 14 m/s in 2 seconds. What is the car’s acceleration?A = ?A = 14 m/s – 0 m/sVi = 0 m/s2 sVf = 14 m/sT = 2 secA = 7 m/s2FOR FULL CREDIT WRITE OUT ALL STEPS AND GIVE ALL UNITSA bicycle rider increases his speed from 5 m/s to 15 m/s in 10 seconds. What is his acceleration?A snail was moving at 2 inches/minute when it noticed a bird. The snail increased it’s pace to 5 inches/minute over a time period of 3 seconds. What is the acceleration of the snail? Name: ___________________________________(p.2 of 5) Math Set #8 Average Acceleration FOR FULL CREDIT WRITE OUT ALL STEPS AND GIVE ALL UNITSA ball rolling down a hill for 9 seconds accelerates from 3 m/s to 34.5 m/s. What is the acceleration of the ball?Caitlin is standing still. She sees a soccer ball flying at her and starts to run toward it. 6 seconds later Caitlin is traveling at 12 ft/sec. What was her acceleration?A spider crawls at a rate of 3 cm/s. The spider speeds up over 10 seconds to a pace of 5 cm/s. What was the acceleration of the spider?CHALLENGE:A person driving a car at 55 miles/hour slowed down over 1 hour to a pace of 45 miles/hour. Is the car accelerating? If the car is accelerating, calculate the acceleration.Name: ___________________________________(p.3 of 5)Math Set #8 Net Force 10 N8 N8 N50 NResulting VectorMotion is to the left40 NWrite a Resulting Force Arrow for each situation and include the number of Newtons.Example: ANSWER300 N 150 N 125 N 125 N 100 N 100 N 125 N 25 N 1.2. Name: ___________________________________(p.4 of 5)Math Set #8 Net Force Write a Resulting Force Arrow for each situation and give the number of Newtons. Write your answers to the right of the diagram. Write numbers for the top two problems, but only use an arrow for the bottom two examples.3 N 4 N 25 N 12 N 10 N 8 N 5 N 25 N 150 N 125 N 125 N 100 N 125 N 125 N Name: ___________________________________(p. 5 of 5)Math Set #8 Gravity, Weight, and Mass Fill in the blank1. A ________________________________________ is used to measure mass.2. A ________________________________________ is used to measure weight.3. The metric unit for mass is _________________.4. The metric unit for weight is _________________.SHOW ALL STEPS AND INCLUDE ALL UNITS FOR FULL CREDIT (use extra paper if needed)On the surface of the earth 100g = 10 N (HINT: use this like a conversion factor)A woman is found to be 90 kilograms. What is her mass? What is her weight?A rock is 50 grams. What is the mass of the rock? What is its weight?On the moon gravity is less strong because the moon has less mass. On the surface of the moon 100g = 0.7 N.On the moon, what is the mass of the woman in example 6? What is her weight on the moon?On the moon, what is the mass of the rock in problem 7? What is its weight on the moon?Name: ___________________________________(p. 1 of 4)Math Set #9 Newton’s Law of Gravity1. The gravity of earth causes a constant acceleration of _______________________________ on the near the surface of the earth. (Be sure to include units)Gravity = acceleration = change in velocityTime it takes for the velocity to changeG = ? velocity TREMEMBER: Change in velocity is final velocity minus initial velocity. Do these problems just like you did the acceleration problems in math set #142. How would you rearrange this equation to calculate velocity?3. How would you rearrange this equation to calculate time?4. A penny at rest is dropped from the top of a tall stairwell. What is the penny’s velocity after it has fallen for two seconds?5. The same penny hits the ground in 4.5 seconds. What is the penny’s velocity as it hits the ground?6. A marble at rest is dropped from a tall building. The marble hits the ground with a velocity of 98 m/s. How long is the marble in the air?7. An acorn at rest falls from an oak tree. The acorn hits the ground with a velocity of 14.7 m/s. How long did it take the acorn to land?Name: ___________________________________(p.2 of 4)Math Set# 9 Newton’s Second LawForce = mass x accelerationF = m x a1. What metric unit is used for mass in Newton’s Law? 2. What metric units are used for acceleration in Newton’s Law? 3. What metric units are used for force? 4. How would you rearrange this equation to find mass?5. How would you rearrange this equation to find acceleration?6. What is the acceleration of a 7 kg mass if a force of 68.6 N is used to move it?7. What force is necessary to accelerate a 1,250 kg car at a rate of 40 m/s2?8. Zookeepers carry a stretcher that holds a sleeping lion. The total mass of the lion and the stretcher is 175 kg. The lion’s forward acceleration is 2 m/s2. What is the force necessary to produce this acceleration? Name: ___________________________________(p.3 out of 4)Math Set #9 MomentumMomentum = mass x velocityP = m x vWhat is the metric unit used for mass in this equation? What are the metric units used for velocity in this equation? What are the metric units used for momentum in this equation? How would you rearrange this equation to solve for mass? How would you rearrange this equation to solve for velocity?The more momentum an object has, the it is to start an object moving, stop the object when it is already moving, and change the direction the object is moving.What is the momentum of a 6 kg bowling ball that is moving at 10 m/s down the alley toward the pins?An 85 kg man is jogging with a velocity of 2.6 m/s to the north. Nearby, a 65 kg person is skateboarding and is traveling with a velocity of 3 m/s north. Which person has a greater momentum? Name: ___________________________________(p.4 out of 4)Math Set #9 Momentum1. A 50 kg child has a momentum of 150 kg x m What is the child’s velocity?s2. An object is moving at a velocity of 2 m/s has a momentum of 1,200 kg x m What is its mass? s 3. A pool cue ball with a mass of 0.16 kg is rolling at a velocity of 4 m/s. What is the momentum of the cue ball?4. Is momentum a force? How do you know?Name: ___________________________________(p.1 of 3)Math Set#10 Converting Review and PracticeWrite the conversion factors that would be used to convert the following:Meters to millimetersCentimeters to metersKilometers to metersGrams to kilogramsMilligrams to gramsMilliliters to litersMilliliters to cubic centimetersCentimeters to inchesPounds to kilogramsMiles to kilometersGallons to litersName: ___________________________________(p.2 of 3)Math Set #10 Converting Review and PracticeUse the procedure in your notebook to perform the following conversions. Include all steps in order to get credit. ANSWERS THAT DO NOT SHOW WORK ARE WRONG. ANSWERS WITHOUT UNITS ARE WRONG.Perform the following conversions, showing all steps120 cm = _______________ m120 cm = _______________ mm10 km = ________________ m2260 g = _______________ kg12,000 mg = __________ g120 ml = _______________ cc7650 cc = _______________ L2 L = ____________________ ccName: ___________________________________(p.3 of 3)Math Set#10 Converting Review and PracticeUse the procedure in your notebook to perform the following conversions. Include all steps in order to get credit. ANSWERS THAT DO NOT SHOW WORK ARE WRONG. ANSWERS WITHOUT UNITS ARE WRONG.Perform the following English to Metric conversions. Round to the nearest whole number.33.02 cm = ________________ in6.69 in = ___________________ cm311.26 LB = _______________ kg2.718 kg = _________________ Lb9.654 miles = _____________ km40.225 km = ______________ mile Name: ____________________________________(1 of 3)Math Set # 11 AreaArea of a Square = side x sideArea of a Rectangle = width x heightArea of a Triangle = ? base x heightOne American UNIT for area is ______________________________.One Metric UNIT for area is ____________________________.Using a ruler draw a square with two-inch sides. Next to that square draw a square with 2-centimeter sides. Under each square calculate the area including units. Make sure there is a unit next to every number. Calculate the area of shape INCLUDING writing the formula and making sure every number has a unit next to it.A square with a side of 5 meters.A rectangle with a width of 2 centimeters and a length of 10 centimeters.A triangle with a height of 2 centimeters and a base of 10 centimeters.Name: ____________________________________(2 of 3)Math Set # 11 PressurePressure = Force divided by Area ( P = F/A)What does Force equal (rearrange the equation)?What does Area equal (rearrange the equation)?The Metric unit for force is: __________________________________________The American unit for force is: _______________________________________ The Metric unit for Pressure is: ______________________________________The American unit for Pressure is: __________________________________Example of Pressure Calculation: Harold weighs 600 Newtons (about 134 pounds). His shoes take up an area on the floor of 0.054 square meters (about 84 square inches). What pressure does Harold exert on the floor?Edward weighs 453 Newtons. His shoes cover an area of 0.05 square meters. Find out what pressure Edward exerts on the floor. SHOW ALL WORK.Melissa weighs 380 Newtons. Her stiletto heels cover an area of .02 square meters. Find out what pressure Melissa exerts on the floor. SHOW ALL WORK.Name: ____________________________________(3 of 3)Math Set # 11 PressureIn Denver, Colorado, the Earth’s atmosphere has a force of about 12 pounds per square inch (psi). Use that value in order to complete the table showing how the size of the area affects the total force of the atmosphere. (Hint: use the formula Force = Pressure x Area)Square Dimensions(inches)Area (inches2)Force (pounds)1 x 11122 x 23 x 34 x 45 x 56 x 67 x 78 x 89 x 910 x 10Inside a tornado the air pressure is 80,000 pascals (Newton/meter2). Suppose this tornado suddenly envelopes a house which has n internal air pressure of 100,000 pascals. What is the pressure difference?What would be the net force acting on an external wall that is 12 meters high and 10 meters long? Is the house likely to suffer less damage if all the windows and doors are left open? Why?Name: ____________________________________(1 of 3)Math Set # 12 BouyancyThe buoyancy principle states that buoyant force is equal to the weight of the fluid that was displaced. It will be assumed that all of the problems occur near the surface of the earth where gravity is an average 9.8 m/s2. It will also be assumed that all water has a density of 1 g/ml unless the problem states a different density.REMEMBER:Density = mass/volume (mass = density x volume)Weight = mass (in kilograms) x 9.8 m/s2 SHOW ALL STEPS/FORMULAS. MAKE SURE THERE IS A UNIT NEXT TO EVERY #.PROBLEM: A box with a volume of 20 mL is completely submerged in water. What is the volume of the displaced water?What is the mass of the displaced water? (use 1 ml pure water = 1 gram water)?What is the weight of the displaced water? (use weight = mass in kg x 9.8 m/s2)What is the buoyant force of the water on the box? (buoyant force = weight of displaced water.)What would the box have to weigh in order to sink in the water?What would the box have to weigh in order to float in the water?Name: ____________________________________(2 of 3)Math Set # 12 BouyancySHOW ALL STEPS/FORMULAS. MAKE SURE THERE IS A UNIT NEXT TO EVERY #.A student has a mass of 70 kg and a volume of 67 liters (67,000 mL). He is submerged in water.What is his weight?What is the volume of the displaced water?What is the mass of the displaced water?What is the weight of the displaced water?What is the buoyant force on the student?Draw a force diagram showing thebuoyant force as an upward arrow and weight as downward arrow. What is the resulting force?A second student has the same volume as the first, but only weighed 600 N. Draw a force diagram showing this situation including the resulting force.Name: ____________________________________(3 of 3)Math Set # 12 Pressure/Bouyancy ReviewWhy do snowshoes make it easier for you to walk in the snow?What is the pressure your feet exert on the floor if you weigh 160 pounds and are standing on both feet covering an area of 40 square inches?If you stand on only one foot on a bathroom scale does your force change?If you want to increase pressure you ______________________(increase or decrease) area or _________________________________ (increase or decrease) force.An object displaces 75 milliliters of water and has a mass of 100 grams. What is the buoyant force? Draw a force diagram showing the buoyant force and gravity. Include the resulting force. (Show all your work… use the back of the paper if necessary) ................
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