Quiz 1: Measurement and Problem Solving
Physics & Astronomy
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The physical quantities are introduced for the purpose of measurements. The fundamental physical quantities are the independent physical quantities and all other physical quantities depend on these fundamental quantities. The SI units of fundamental physical quantities are nothing but base units in the SI system. The seven fundamental physical quantities are mass, length, time, current, temperature, amount of substance and intensity of light. The base units in the SI system are: Kilogram, meter, second, ampere, kelvin, mole and candela. Any units other these can be expressed in terms of these units. That is, the base units are enough to express any other units, using different combinations among them. This is why there are not more SI base units.
Q 2Q 2
The metric system is a decimal (base-10) system, and the British system is, in part, a duodecimal (base-12) system. Discuss the ramifications if our monetary system had a duodecimal base. What would be the possible values of our coins if this were the case
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The metric system is a base-10 (decimal) system and British system is a base-12(duodecimal) system.
In the decimal system (base-10), a dime is equal to 10 cents.
Here,
is symbol of penny.
One dollar is equal to 10 dimes.
Substitute
for dime in the above equation.
Similarly, in a duodecimal (base-12) system, a dime is equal to 12 ¢.
A dollar is equal to 12 dimes.
Substitute
for dime in the above equation.
Rewrite equation for
.
Therefore, a penny would be
of a decimal dollar.
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Multiple Choice
International system of units is the recent description of metric system and it is abbreviated as SI. The SI system consists of both base units and derived units.
There are seven base units of SI system. They are as follows:
Thus, there are seven base units in the SI system.
Hence, the correct option is
.
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Q 5Q 5
(a) In the British system, 16 oz = 1 pt and 16 oz = 1 lb. Is something wrong here Explain. Here's an old one: A pound of feathers weighs more than a pound of gold. How can that be [ Hint : Look up ounce in the dictionary.]
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Q 6Q 6
The only SI standard represented by material standard or artifact is the (a) meter, (b) kilogram, (c) second, (d) electric charge.
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Multiple Choice
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Q 8Q 8
Convert the following: (a) 40 000 000 bytes to MB, (b) 0.5722 mL to L, (c) 2.684 m to cm, and (d) 5 500 bucks to kilobucks.
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Q 9Q 9
Which of the following is the SI base emit for mass: pound, (b) gram, (c) kilogram, or (d) ton
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Q 11Q 11
A sailor tells you that if his ship is traveling at 25 knots (nautical miles per hour), it is moving faster than the 25 mi/h your car travels. How can that be
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Q 12Q 12
Which of the following is not related to a volume of water: (a) kilogram, (b) pound, (c) gram, or (d) tonne
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Q 13Q 13
If a fellow student tells you he saw a 3-cm-long ladybug, would you believe him How about another student saying she caught a 10-kg salmon
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Q 14Q 14
A rectangular container measuring 25 cm × 35 cm × 55 cm is filled with water. What is the mass of this volume of water
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Q 20Q 20
(a) What volume in liters is a cube 20 cm on a side (b) If the cube is filled with water, what is the mass of the water
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Q 21Q 21
Anew technology is concerned with objects the size of what metric prefix: (a) nano -, (b) micro -, (c) mega -, or (d) giga -
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Q 22Q 22
Can unit analysis tell you whether you have used the correct equation in solving a problem Explain.
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Q 23Q 23
Show that the equation x = x o + vt , where v is velocity, x and x o are lengths, and t is time, is dimensionally correct.
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Q 25Q 25
The equation for the area of a circle from two sources is given as A = r 2 and A = d 2 /2. Can unit analysis tell you which is correct Explain.
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Q 26Q 26
If x refers to distance, v o and v to velocities, a to acceleration, and t to time, which of the following equations is dimensionally correct: (a) x = v o t + at 3 , (b) v 2 = v o 2 + 2 at , (c) x = at + vt 2 , or (d) v 2 = v o 2 + 2 ax
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Q 27Q 27
Which of the following metric prefixes is the smallest: micro-, (b) centi-, (c) nano-, or (d) milli-
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Q 29Q 29
Use SI unit analysis to show that the equation A = 4 r 2 , where A is the area and r is the radius of a sphere, is dimensionally correct.
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Q 30Q 30
Both sides of an equation are equal in (a) numerical value, (b) units, (c) dimensions, (d) all of the preceding.
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Q 32Q 32
The general equation for a parabola is y = ax 2 + bx + c , where a, b , and c are constants. What are the units of each constant if y and x are in meters
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Q 33Q 33
Unit analysis of an equation cannot tell you if (a) the equation is dimensionally correct, (b) the equation is physically correct, (c) the numerical value is correct, (d) both b and c.
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Q 35Q 35
You are told that the volume of a sphere is given by V = d 3 /4, where V is the volume and d is the diameter of the sphere. Is this equation dimensionally correct (Use SI unit analysis to find out.)
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Q 36Q 36
A good way to ensure proper unit conversion is to use another measurement instrument, (b) always work in the same system of units, (c) use unit analysis, (d) have someone check your math.
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Q 38Q 38
The correct equation for the volume of a sphere is V = 4 r 3 /3, where r is the radius of the sphere. Is the equation in Exercise correct If not, what should it be when expressed in terms of d
Exercise
You are told that the volume of a sphere is given by V = d 3 /4, where V is the volume and d is the diameter of the sphere. Is this equation dimensionally correct (Use SI unit analysis to find out.)
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Q 39Q 39
You often see 1 kg = 2.2 lb. This expression means that (a) 1 kg is equivalent to 2.2 lb, (b) this is a true equation, 1 lb = 2.2 kg, (d) none of the preceding.
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Q 40Q 40
A popular saying is "Give him an inch and he'll take a mile." What would be the equivalent numerical values and units in the metric system
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Q 41Q 41
The units for pressure ( p ) in terms of SI base units are known to be
. For a physics class assignment, a student derives an expression for the pressure exerted by the wind on a wall in terms of the air density ( ) and wind speed ( v ) and her result is p = v 2. Use SI unit analysis to show that her result is dimensionally consistent. Does this prove that this relationship is physically correct
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Q 42Q 42
You have a quantity of water and wish to express this in volume units that give the largest number. Which of the following units should be used: (a) in 3 , (b) mL, (c) L, or (d) cm 3
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Q 44Q 44
Is the equation for the area of a trapezoid,
, where a is the height and b 1 and b 2 are the bases, dimensionally correct (Fig..)
FIGURE The area of a trapezoid See Exercise.
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Q 45Q 45
Which of the following has the greatest number of significant figures: (a) 103.07, (b) 124.5, (c) 0.09916, or (d) 5.408 × 10 5
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Q 47Q 47
Newton's second law of motion (Section 4.3) is expressed by the equation F = ma , where F represents force, m is mass, and a is acceleration. (a) The ST unit of force is, appropriately, called the newton (N). What are the units of the newton in terms of base quantities (b) An equation for force associated with uniform circular motion (Section 7.3) is F = mv 2 / r , where v is speed and r is the radius of the circular path. Does this equation give the same emits for the newton
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Q 48Q 48
Which of the following numbers has four significant figures: (a) 140.05, (b) 276.02, (c) 0.004 006, or (d) 0.073 004
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Q 49Q 49
How are the number of significant figures determined for the results of calculations involving (a) multiplication, (b) division, (c) addition, and (d) subtraction
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Q 50Q 50
Tire angular momentum ( L ) of a particle of mass m moving at a constant speed v in a circle of radius r is given by L = mvr (Section 8.5). (a) What are the units of angular momentum in terms of SI base units (b) The units of kinetic energy in terms of ST base units are
.
Using SI unit analysis, show that the expression for the kinetic energy of this particle in terms of its angular momentum,
, is dimensionally correct. (c) In the previous equation, the term mr 2 is called the moment of inertia of the particle in the circle. What are the units of moment of inertia in terms of SI base units
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Q 51Q 51
In a multiplication and/or division operation involving the numbers 15 437, 201.08, and 408.0 × 10 5 , the result should have how many significant figures: (a) 3, (b) 4, (c) 5, or (d) any number
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Q 52Q 52
Einstein's famous mass-energy equivalence is expressed by the equation E = mc 2 , where E is energy, m is mass, and c is the speed of light. (a) What are the SI base units of energy (b) Another equation for energy is E = mgh , where m is mass, g is the acceleration due to gravity, and h is height. Does this equation give the same units as in part (a)
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Q 53Q 53
An important step in problem solving before mathematically solving an equation is (a) checking units, (b) checking significant figures, (c) checking with a friend, (d) checking to see if the result will be reasonable.
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Q 55Q 55
Figure 1.8 (top) shows the elevation of a location in both feet and meters. Is the conversion correct
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Q 56Q 56
An important final step in problem solving before reporting an answer is (a) saving your calculations, (b) reading the problem again, (c) seeing if the answer is reasonable, (d) checking your results with another student.
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Q 57Q 57
When you do order-of-magnitude calculations, should you be concerned about significant figures Explain.
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Q 58Q 58
(a) If you wanted to express your height with the largest number, which units would you use: (1) meters, (2) feet, (3) inches, or (4) centimeters Why (b) If you are 600 ft tall, what is your height in centimeters
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Q 59Q 59
In order-of-magnitude calculations, you should (a) pay close attention to significant figures, (b) work primarily in the British system, (c) get results within a factor of 100, express a quantity to the power of 10 closest to the actual value.
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Q 60Q 60
When doing an order-of-magnitude calculation, how accurate can you expect the answer to be Explain.
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Q 61Q 61
If the capillaries of an average adult were unwound and spread out end to end, they would extend to a length over 40 000 mi (Fig. 1.9). If you are 1.75 m tall, how many times your height would the capillary length equal
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Q 62Q 62
The largest organ of the human body is the skin. The total external skin area of the average human covers an area of approximately 2.0 m 2. If you were asked to compute the approximate skin area, how would you go about it ( Hint : see Example 8.18.)
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There is no answer for this question
Q 63Q 63
(a) Compared with a 2-L soda bottle, a half-gallon soda bottle holds (1) more, (2) the same amount of, (3) less soda. (b) Verify your answer for part (a).
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Q 64Q 64
Is the following statement reasonable It took 300 L of gasoline to fill the car's tank. (Justify your answer.)
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Q 65Q 65
(a) A football field is 300 ft long and 160 ft wide. What are the field's dimensions in meters (b) A football is 11.0 to
in. long. What is its length in centimeters
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Q 66Q 66
Is the following statement reasonable A car traveling 30 km/h through a school speed zone exceeds the speed limit of 25 mi/h. (Justify your answer.)
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Q 67Q 67
Suppose that when the United States goes completely metric, the dimensions of a football field are established as 100 m by 54 m. Which would be larger, the metric football field or a current football field (see Exercise), and what would be the difference between the areas
Exercise
(a) A football field is 300 ft long and 160 ft wide. What are the field's dimensions in meters (b) A football is 11.0 to
in. long. What is its length in centimeters
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Q 70Q 70
A submarine is submerged 175 fathoms below the surface. What is its depth in meters (A fathom is an old nautical measurement equal to 2 yd.)
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Q 71Q 71
Driving a jet-powered car, Royal Air Force pilot Andy Green broke the sound barrier on land for the first time and achieved a record land speed of more than 763 mi/h in Black Rock Desert, Nevada, on October 15, 1997 (Fig.). (a) What is this speed expressed in m/s (b) How long would it take the jet-powered car to travel the length of a 300-ft football field at this speed ( Hint: v = d/t. )
FIGURE Record run see Exercise.
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Q 72Q 72
(a) Which of the following represents the greatest speed: (1) 1 m/s, (2) 1 km/h, (3) 1 ft/s (4) 1 mi/h (b) Express the speed 15.0 m/s in mi/h.
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Q 73Q 73
An automobile speedometer is shown in Fig. (a) What would be the equivalent scale readings (for each empty box) in kilometers per hour (b) What would be the 70-mi/h speed limit in kilometers per hour
FIGURE Speedometer readings See Exercise.
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Q 74Q 74
A person weighs 170 lb. (a) What is his mass in kilograms (b) Assuming the density of the average human body is about that of water (which is true), estimate his body's volume in both cubic meters and liters. Explain why the smaller unit of the liter is more appropriate (convenient) for describing a volume of this size.
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Q 75Q 75
If the components of the human circulatory system (arteries, veins, and capillaries) were completely extended and placed end to end, the length would be on the order of 100 000 km. Would the length of the circulatory system reach around the circumference of the Moon If so, how many times
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Q 76Q 76
The human heartbeat, as determined by the pulse rate, is normally about 60 beats/min. If the heart pumps 75 mL of blood per beat, what volume of blood is pumped in one day in liters
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Q 77Q 77
Some common product labels are shown in Fig. From the units on the labels, find (a) the number of milliliters in 2 fl. oz and (b) the number of ounces in 100 g.
FIGURE Conversion factors See Exercise.
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Q 78Q 78
Fig. is a picture of red blood cells seen under a scanning electron microscope. Normally, women possess about 4.5 million of these cells in each cubic millimeter of blood. If the blood flow to the heart is 250 mL/min, how many red blood cells does a woman's heart receive each second
FIGURE Red blood cells See Exercise.
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Q 79Q 79
A student was 1.8 in. long when she was born. She is now 5 ft 6 in. tall and 20 years old. How many centimeters a year did she grow on average
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Q 81Q 81
The density of metal mercury is 13.6 g/cm 3. (a) What is this density as expressed in kilograms per cubic meter (b) How many kilograms of mercury would be required to fill a 0.250-L container
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Q 82Q 82
The Roman Coliseum used to be flooded with water to re-create ancient naval battles. Assuming the circular floor be 250 m in diameter and the water to have a depth of 10 ft, (a) how many cubic meters of water are required (b) How much mass would this water have in kilograms (c) How much would the water weigh in pounds
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Q 83Q 83
In the Bible, Noah is instructed to build an ark 300 cubits long, 50.0 cubits wide, and 30.0 cubits high (Fig.). Historical records indicate a cubit is equal to half a yard. (a) What would be the dimensions of the ark in meters (b) What would be the ark's volume in cubic meters To approximate, assume that the ark is to be rectangular.
FIGURE Noah and his ark See Exercise.
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Q 84Q 84
Express the length 50 500 µ m (micrometers) in centimeters, decimeters, and meters, to three significant figures.
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Q 85Q 85
Using a meterstick, a student measures a length and reports it to be 0.8755 m. What is the smallest division on the meterstick scale
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Q 86Q 86
Determine the number of significant figures in the following measured numbers: (a) 1.007 m, (b) 8.03 cm, (c) 16.272 kg, (d) 0.015 µ s (microseconds).
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Q 87Q 87
Express each of the numbers in Exercise with two significant figures.
Exercise
Determine the number of significant figures in the following measured numbers: (a) 1.007 m, (b) 8.03 cm, (c) 16.272 kg, (d) 0.015 µ s (microseconds).
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Q 88Q 88
Round the following numbers to two significant figures: (a) 95.61, (b) 0.00208, (c) 9438, (d) 0.000344
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Q 89Q 89
Which of the following quantities has three significant figures: (a) 305.0 cm, (b) 0.0500 mm, (c) 1.000 81 kg, (d) 8.06 × 10 4 m 2
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Q 90Q 90
The cover of your physics book measures 0.274 m long and 0.222 m wide. What is its area in square meters
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Q 91Q 91
The interior storage compartment of a restaurant refrigerator measures 1.3 m high, 1.05 m wide, and 67 cm deep. Determine its volume in cubic feet.
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Q 92Q 92
The top of a rectangular table measures 1.245 m by 0.760 m. (a) The smallest division on the scale of the measurement instrument is (1) m, (2) cm, (3) mm. Why (b) What is the area of the tabletop
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Q 93Q 93
The outside dimensions of a cylindrical soda can are reported as 12.559 cm for the diameter and 5.62 cm for the height. (a) How many significant figures will the total outside area have: (1) two, (2) three, (3) four, or (4) five Why (b) What is the total outside surface area of the can in square centimeters
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Q 94Q 94
Express the following calculations using the proper number of significant figures: (a) 12.634 + 2.1,(b) 13.5 2.134, (c) (0.25 m) 2 , (d)
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Q 95Q 95
In doing a problem, a student adds 46.9 m and 5.72 m and then subtracts 38 m from the result. (a) How many decimal places will the final answer have: (1) zero, (2) one, or (3) two Why (b) What is the final answer
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Q 96Q 96
Work this exercise by the two given procedures as directed, commenting on and explaining any difference in the answers. Use your calculator for the calculations. Compute p = mv , where v = x/t , given x = 8.5 m, t = 2.7 s, and m = 0.66 kg. (a) First compute v and then p. (b) Compute p = mx/t without an intermediate step. (c) Are the results the same If not, why
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Q 97Q 97
A corner construction lot has the shape of a right triangle. If the two sides perpendicular to each other are 37 m long and 42.3 m long, what is the length of the hypotenuse
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Q 98Q 98
The lightest solid material is silica aerogel, which has a typical density of only about 0.10 g/cm 3. The molecular structure of silica aerogel is typically 95% empty space. What is the mass of 1 m 3 of silica aerogel
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Q 99Q 99
A cord of wood is a volume of cut wood equal to a stack 8.0 ft long, 4.0 ft wide, and 4.0 ft high. How many cords are there in 3.0 m 3
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Q 100Q 100
Nutrition Facts labels now appear on most foods. An abbreviated label concerned with fat is shown in Fig.. When burned in the body, each gram of fat supplies 9 Calories. (A food Calorie is really a kilocalorie, as will be learned in Chapter 11.) (a) What percentage of the Calories in one serving is supplied by fat (b) You may notice that our answer doesn't agree with the listed Total Fat percentage in Fig.. This is because the given Percent Daily Values are the percentages of the maximum recommended amounts of nutrients (in grams) contained in a 2000-Calorie diet. What are the maximum recommended amounts of total fat and saturated fat for a 2000-Calorie diet
FIGURE Nutrition Facts See Exercise.
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Q 101Q 101
The thickness of the numbered pages of a textbook is measured to be 3.75 cm. (a) If the last page of the book is numbered 860, what is the average thickness of a page (b) Repeat the calculation by using order-of-magnitude calculations.
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Q 102Q 102
The mass of the Earth is 5.98 × 10 24 kg. What is the average density of the Earth in standard units
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Q 103Q 103
To go to a football stadium from your house, you first drive 1000 m north, then 500 m west, and finally 1500 m south. (a) Relative to your home, the football stadium is (1) north of west, (2) south of east, (3) north of east, (4) south of west. (b) What is the straight-line distance from your house to the stadium
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Q 104Q 104
Two chains of length 1.0 m are used to support a lamp, as shown in Fig.. The distance between the two chains along the ceiling is 1.0 m. What is the vertical distance from the lamp to the ceiling
FIGURE Support the lamp See Exercise.
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Q 105Q 105
Tony's Pizza Palace sells a medium 9.0-in. (diameter) pizza for $7.95, and a large 12-in. pizza for $13.50. Which pizza is the better buy
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Q 106Q 106
Two students go into Tony's Pizza Palace and order a 12-in. (diameter) pizza. Shortly thereafter, the waitress brings an 8-in. pizza special. She explains that the 12-in. pizza was given to someone else by mistake and they could have the 8-in. now and she would bring another 8-in. shortly to make up for the missing 12-in. pizza. Was this a good deal
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Q 107Q 107
In Fig., which black region has the greater area, the center circle or the outer ring
FIGURE Which black area is greater See Exercise.
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Q 108Q 108
The Channel Tunnel, or "Chunnel," which runs under the English Channel between Great Britain and France, is 31 mi long. (There are actually three separate tunnels.) A shuttle train that carries passengers through the tunnel travels with an average speed of 75 mi/h. On average, how long, in minutes, does the shuttle take to make a one-way trip through the Chunnel
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Q 109Q 109
Human adult blood contains, on average, 7000/mm 3 white blood cells (leukocytes) and 250 000/mm 3 platelets (thrombocytes). If a person has a blood volume of 5.0 L, estimate the total number of white cells and platelets in the blood.
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Q 110Q 110
The average number of hairs on the normal human scalp is 125 000. A healthy person loses about 65 hairs per day. (New hair from the hair follicle pushes the old hair out.) (a) How many hairs are lost in one month (b) Pattern baldness (top-of-the-head hair loss) affects about 35 million men in the United States. If an average of 15% of the scalp is bald, how many hairs are lost per year by one of these "bald is beautiful" people
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Q 111Q 111
A car is driven 13 mi east and then a certain distance due north, ending up at a position 25° north of east of its initial position. (a) The distance traveled by the car due north is (1) less than, (2) equal to, (3) greater than 13 mi. Why (b) What distance due north does the car travel
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Q 112Q 112
At the Indianapolis 500 time trials, each car makes four consecutive laps, with its overall or average speed determining that car's place on race day. Each lap covers 2.5 mi (exact). During a practice run, cautiously and gradually taking his car faster and faster, a driver records the following average speeds for each successive lap: 160 mi/h, 180 mi/h, 200 mi/h, and 220 mi/h. (a) Will his average speed be (1) exactly the average of these speeds (190 mi/h), (2) greater than 190 mi/h, or (3) less than 190 mi/h Explain. (b) To corroborate your conceptual reasoning, calculate the car's average speed.
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Q 113Q 113
Approximately 118 mi wide, 307 mi long, and averaging 279 ft in depth, Lake Michigan is the second- largest Great Lake by volume. Estimate its volume of water in cubic meters.
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Q 114Q 114
In the Tour de France, a bicyclist races up two successive (straight) hills of different slope and length. The first is 2.00 km long at an angle of 5° above the horizontal. This is immediately followed by one 3.00 km long at 7°. (a) What will be the overall (net) angle from start to finish: (1) smaller than 5°, (2) between 5° and 7°, or (3) greater than 7° (b) Calculate the actual overall (net) angle of rise experienced by this racer from start to finish, to corroborate your reasoning in part (a).
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Q 115Q 115
A student wants to determine the distance from the lakeshore to a small island (Fig.). He first draws a 50-m line parallel to the shore. Then, he goes to the ends of the line and measures the angles of tire lines of sight from the island relative to the line he has drawn. The angles are 30° and 40°. How far is the island from the shore
FIGURE Measuring with lines of sight See Exercise.
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Q 116Q 116
A farmer owns a piece of land in the shape of an equilateral triangle, 200 m on a side, which is totally fenced in. He wishes to construct an additional fence parallel to the side fronting the road (Fig.) so that the area fronting the road takes up one-third of the total area. This area will be for Iris horses. On the remaining two-thirds he plans to construct his dream home. How far back from the road (shown as the distance h ) should the fence be located
FIGURE Don't fence me in See Exercise.
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Q 117Q 117
In a radioactivity experiment, a solid lead brick (with same measurements as a patio brick, 2.00 in. × 4.00 in. × 8.00 in., except with a density that is 11.4 times that of water) is to be modified to hold a solid cylindrical piece of plastic. To accomplish this, the machinists are told to drill a cylindrical hole 2.0 cm in diameter through the center of the brick parallel to the longest side of the brick. (a) What is the mass of lead (in kilograms) removed from the brick (b) What percentage of the original lead remains in the brick (c) Assuming the cylindrical hole is completely filled with plastic (with a density twice that of water), determine the overall (average) density of the brick/plastic combination after fabrication is complete.
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Q 118Q 118
A spherical shell is formed by taking a solid sphere of radius 20.0 cm and hollowing out a spherical section from the shell's interior. Assume the hollow section and the sphere itself have the same center location (that is, they are concentric). (a) If the hollow section takes up 90.0 percent of the total volume, what is its radius (b) Win at is the ratio of tine outer area to the inner area of the shell
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Q 119Q 119
Two separate seismograph stations receive indication of an earthquake in the form of a wave traveling to them in a straight line from the epicenter and shaking the ground at their locations. Station B is 50 km due east of station A. The epicenter is located due north of station A and 30° north of due west from station B. (a) Draw a sketch and use it to determine the distance from the epicenter to A. (b) Determine the distance from the epicenter to B. (c) Station C is located an additional 20 km east of B. At what angle does C report the direction of the epicenter to be
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Q 120Q 120
You are sailing a radio-controlled model powerboat on a perfectly circular pool of water. The boat travels at a constant 0.500 m/s. It takes 30.0 s to make the trip from one side of the pool, through the center, to the other side. (a) How long would it take the boat to travel completely around the edge of the pool (b) If the pool is uniformly 1.50 m deep, how many gallons of water does it hold
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Q 121Q 121
A certain material has a density of 9.0 g/cm 3. It is formed into a solid rectangular brick with dimensions 1.0 cm × 2.0 cm × 4.0 cm. (a) What is its mass in kilograms (b) If you wanted to make a cube of this same material containing twice the mass of this brick, what would be the length of one side of the cube
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