The Eiffel Tower has a mass of 10,000,000 kg. A 100:1 scale model of the tower made from the same material will have a mass of (A) 100,000 kg (B) 10,000 kg (C) 1,000 kg (D) 100 kg (E) 10 kg (F) 1 kg The paths crossed for three men -- A, B, and C -- walking through woods. It was a cold night. They decided to light a fire and rest by it for the night. They set out to bring some firewood. A came back with 5 logs of wood, B brought 3 logs, but C came back empty-handed. C requested that they let him rest by the fire and promised to pay them some money in the morning. In the morning C paid them $8. How should A and B split the money fairly? (A) A $7; B $1 (B) A $6; B $2 (C) A $5; B $3 (D) A $4; B $4 (E) None of these
An insect is climbing up a 30 ft. vertical wall. Starting from the bottom, the insect climbs up 3 ft. during the day and slips down 2 ft. during the night. In how many days will the insect reach the top of the wall? (A) 31 days (B) 30 days (C) 29 days (D) 28 days (E) 27 days (F) Never Two trains are moving toward each other with speeds of 17 mph and 43 mph. How far apart are they 1 minute before they pass each other? (A) 60 miles (B) 30 miles (C) 6 miles (D) 3 miles (E) 2 miles (F) 1 mile
Weight of the Flies. The weight of a closed jar is W while the flies inside it are flying around. What will be the weight of the jar if the flies settle down inside the jar? (A) Equal to W (B) Less than W (C) Less than W
PHYSICS BASICS Theory-explain observations. Applications- concepts are used to help solve other problems Models-help to understand the concepts The physics course is made up of three main areas of study
PHYSICAL QUANTITIES The study of Physics requires us to measure physical quantities and UNITS are used to denote what quantities we are measuring. It is important that after every measurement we place a UNIT to state what we are measuring otherwise the quantity measured is useless. There are 7 units for measurement. Devised by the Systeme International d’Unites’. These are specific units for specific measurements.
SI units are based on 3 fundamental quantities -Mass kg. M. -Length m. L. -Time s. T. Area =L x L = L ² Velocity = L / T = LT -1 Energy = ½ mv ² = M x ( L/T) ² =ML²/T² = units joules Area =L x L = L ² Velocity = L / T = LT - 1 Energy = ½ mv ² = M x ( L/T) ² =ML²/T² = units joules
Physical quantities & their units QuantitySI Unit NameSymbol(s)NameSymbol Length Mass Time Electric current Temperature Luminous intensity Amount of substance I, x, y d, etc M, m T, t I T I N metre kilogram second ampere kelvin candela mole m kg s A K cd mol
Often the size of the quantity Physicists measure is very large or very small. To help make the numbers easier to use prefix multipliers are used. You know it as standard form. These are mulitples of ten. You must learn these and be able to convert from one to the other. The standard prefix multipliers are: These are mulitples of ten. You must learn these and be able to convert from one to the other. The standard prefix multipliers are:
Standard Prefix Multipliers PowerPrefixSymbol 10 9 10 6 10 3 10 -3 10 -6 10 -9 10 -12 GMkmnpGMkmnp Is the Greek letter pronounced ‘mew’ If positive power, move decimal place to the right. If negative power, move decimal place to the left Giga Mega Kilo Milli Micro Nano Pico
E XAMPLE Q UESTIONS 1. Change 8 km to m 2. How many micrograms are there in a kilogram? 3. Write 2.8x10 10 watts in gigawatts Solutions: 1.8 km= 8 x 10 3 m = 8000m 2.1 kg= 1 x 10 3 g = 1 x 10 3 x 10 6 g = 10 9 g 3.2.8 x 10 10 W= 2.8 x 10 x 10 9 W = 28 x 10 9 W = 28 GW Solutions: 1.8 km= 8 x 10 3 m = 8000m 2.1 kg= 1 x 10 3 g = 1 x 10 3 x 10 6 g = 10 9 g 3.2.8 x 10 10 W= 2.8 x 10 x 10 9 W = 28 x 10 9 W = 28 GW
SIGNIFICANT FIGURES Certain pieces of measuring equipment have limits to how accurately they can measure quantities. This is shown by using specific sig. figs. A 30 cm ruler can measure up to 1mm only. Therefore 15.7 cm in SI units must be written as 0.157m. This measurement is to 3 sig. figs. 0.1570 means you can measure to less than 1mm, which you can’t.
the measurement should be the least number of significant figures of the data values used. Multiplication or Division the measurement should be rounded to the least number of decimal places of the data values used. Addition or Subtraction
E XAMPLE : SOLUTION a.Perimeter of the plate: = 15.4 + 0.94 + 15.4 + 0.94 = 32.68 = 32.7 cm (to 1 decimal point) b.Area of the plate: = 15.4 x 0.94 = 14.476 = 14 cm 2 (to 2 sf) A metal plate has the following dimensions: Length 15.4cm. Width 0.94cm. Calculate : Perimeter of the plate Area of the plate
EXERCISES Read through pages 4-9 from Rutter. 4: all 5: 1,2,3 6: 1-4 8: all 9: all
As Physicists you now have to question the validity of the data you collect. Can you accept it or should you do it again. When looking at error we firstly have to deal with whether there is an error in the first place. Two terms that should be employed when looking at data are PRECISE and ACCURATE. DATA ERROR
What do these terms mean: PPRECISE : ccluster of data but possibly in the wrong place. AACCURATE : ddata which is grouped around the right place. AACCURATE & PRECISE: data which is clustered in the right place and close together.
The dictionary definitions of these two words do not clearly make the distinction as it is used in the science of measurement. Accurate means "capable of providing a correct reading or measurement." In physical science it means 'correct'. A measurement is accurate if it correctly reflects the size of the thing being measured. Precise means "exact, as in performance, execution, or amount. "In physical science it means "repeatable, reliable, getting the same measurement each time." We can never make a perfect measurement. The best we can do is to come as close as possible within the limitations of the measuring instruments.
Let's use a model to demonstrate the difference. Suppose you are aiming at a target, trying to hit the bull's eye (the center of the target) with each of five darts. Here are some representative pattern of darts in the target.
This is a random like pattern, neither precise nor accurate. The darts are not clustered together and are not near the bull's eye.
This is a precise pattern, but not accurate. The darts are clustered together but did not hit the intended mark.
This is an accurate pattern, but not precise. The darts are not clustered, but their 'average' position is the center of the bull's eye.
This pattern is both precise and accurate. The darts are tightly clustered and their average position is the center of the bull's eye.
There are two types of error 1. Random error - are statistical fluctuations (in either direction) in the measured data due to the precision limitations of the measurement device. Random errors usually result from the experimenter's inability to take the same measurement in exactly the same way to get exact the same number. 2. Systematic error - by contrast, are reproducible inaccuracies that are consistently in the same direction. Systematic errors are often due to a problem which persists throughout the entire experiment.
Identification of these random and systematic errors and how you go about alleviating them is a major component of your internal 2.1 achievement standard.
H OW DO WE IMPROVE THE ACCURACY OF OUR MEASUREMENT ? 1. Take repeated readings and average them 2. Take a multiple measurement of some quantity and then divide by the number of items being measured 3. Adjust the zero reading or subtract value from the readings when using that instrument 4. Read directly from in front of the scale
Systematic and random errors refer to problems associated with making measurements. Mistakes made in the calculations or in reading the instrument are not considered in error analysis. It is assumed that the experimenters are careful and competent! Systematic and random errors refer to problems associated with making measurements. Mistakes made in the calculations or in reading the instrument are not considered in error analysis. It is assumed that the experimenters are careful and competent!
CONVERTING RELATIONSHIPS TO EQUATIONS In order to produce an equation from data the following steps should be observed: GRAPHING SKILLS
5. Calculate the gradient of the straight line using the rise/run method. 6. This is ‘m’ in the ‘y = mx + c’ equation.7. In most cases ‘c’ = 0 so can be ignored.8. Rewrite the equation with the function of ‘x’ and the new gradient. 1.Tabulate your raw data and sketch this on a graph. 2. Decide what relationship has been produced i.e. y x; y 1/x; y x 2 e.t.c.3. Do the function to x i.e. if y 1/x then do x -1 to all the x values. 4. Plot y versus 1/x and this should produce a straight line if you have drawn it correctly.
C OMMON G RAPHS y x y 1/x y x ² y 1/x ²
Y is proportional to X When X changes by certain factor, Y changes by the same.
Y is inversely proportional to X When X is multiplied by a certain factor, Y is divided by the same factor
Y is proportional to the square of X As X is multiplied by a certain factor, Y is multiplied by the square of that factor
Y is inversely proportional to the square of X As X increases by a certain factor, then Y decreases by 1/ the square of that factor E.g. X doubled, Y decreases by 1/4
Using these skills do exercises from Page: 10 -20 RUTTER Using these skills do exercises from Page: 10 -20 RUTTER