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Physics for Scientists and Engineers with Modern Physics, 3e Knight

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Ch 01 HW Due: 11:59pm on Tuesday, January 28, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy

Tactics Box 1.1 Vector Addition Description: Knight Description: Knight Tactics Box 1.1 Vector Addition is illustrated. (vector applet) Learning Goal: To practice Tactics Box 1.1 Vector Addition. Vector addition obeys rules that are different from those for the addition of two scalar quantities. When you add two vectors, their directions, as well as their magnitudes, must be taken into account. This Tactics Box explains how to add vectors graphically graphically..

TACTICS TACT ICS BOX 1.1 Vector addition

⃗ to A ⃗ , perform these steps: To add B

.⃗ 1. Draw A ⃗ at the tip of A .⃗ 2. Place the tail of B

⃗ to the tip of B .⃗ This is 3. Draw an arrow from the tail of A

http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2736256

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⃗ + B ⃗ . vector A

Part A ⃗ Create the vector R

⃗ + B ⃗ by following the steps in the Tactics Box above. When moving vector B ⃗, keep in =A

mind that its direction should remain unchanged. The location, orientation, and length of your vectors will be graded. ANSWER:

Part B ⃗ Create the vector R

⃗ + D ⃗ by following the steps in the Tactics Box above. When moving vector D ⃗ , keep in = C

mind that its direction should remain unchanged. The location, orientation, and length of your vectors will be graded. ANSWER:


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Tactics Box 1.3 Finding the Acceleration Vector Description: Knight Tactics Box 1.3 Finding the Acc eleration Vector is illustrated. (vector applet) Learning Goal: To practice Tactics Box 1.3 Finding the Acceleration Vector. Suppose an object has an initial velocity vn⃗ at time tn and later, at time tn+1, has velocity vn⃗ +1 . The fact that the velocity changes tells us the object undergoes an acceleration during the time interval ∆t = tn+1 − tn. From the definition of average acceleration,

a⃗ =

v n⃗ +1− v n⃗

tn+1−tn

=

⃗ ∆ v ∆t

,

we see that the acceleration vector points in the same direction as the vector ∆ v ⃗. This vector is the change in the velocity ∆ v ⃗ = vn⃗ +1 − vn⃗ , so to know which way the acceleration vector points, we have to perform the vector subtraction vn⃗ +1 − vn⃗ . This Tactics Box shows how to use vector subtraction to find the acceleration vector.

TACTICS BOX 1.3 Finding the acceleration vector

To find the acceleration as the velocity changes from vn⃗ to v n⃗ +1 :


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1. Draw the velocity vector vn⃗ +1 .

2. Draw − vn⃗ at the tip of vn⃗ +1 . 3. Draw ∆ v⃗

= vn⃗ +1 − vn⃗ = vn⃗ +1 + (− vn⃗ ) . This is the

direction of a .⃗ 4. Return to the original motion diagram. Draw a vector at the middle point in the direction of ∆ v ;⃗ label it a.⃗ This is the average acceleration at the midpoint between

vn⃗ and vn⃗ +1 .

Part A Below is a motion diagram for an object t hat moves along a linear path. The dots represent the position of the object at three subsequent instants, t1 , t 2 , and t 3 . The vectors v2⃗ 1 and v3⃗ 2 show the average velocity of the object for the initial time interval, ∆t21 = t 2 − t1 , and the final time interval, ∆t32 = t 3 − t2 , respectively. Draw the vector → ⃗ representing the change in average velocity of the object during the total time −v 21 and the acceleration vector a interval ∆t

= t3 − t1 . Assume for this problem that ∆t = 1 s.

The orientation and length of the vectors will be graded. The location of the vectors will not be graded.

Hint 1. How to draw the acceleration vector → → → First, draw −v 21 . Draw −v 21 starting at the tip of v2⃗ 1 and ending at its tail. Then, move −v 21, with the same orientation, so that its tail is at the tip of v3⃗ 2 . Use the vector info button to make sure that the lengths of v 2⃗ 1 → → ,⃗ starts at the tail of and −v 21 are equal. The acceleration vector, a v3⃗ 2 and ends at the tip of −v 21.

ANSWER:


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Part B Below is another motion diagram for an object that moves along a linear path. The dots represent the position of the object at five subsequent instants, t1 , t 2 , t3 , t4 , and t 5 . The vectors v2⃗ 1 , v3⃗ 2 , v4⃗ 3 , and v 5⃗ 4 represent the average → → velocity of the object during the four corresponding time intervals. Draw the velocity vectors −v 21 and −v 43 and the 5⃗ 3 representing the changes in average velocity of the object during the time intervals acceleration vectors a 3⃗ 1 and a ∆t31

= t3 − t 1

and ∆t53

= t5 − t3 , respectively. Assume for this problem that ∆t31 = ∆t53 = 1 s.

The orientation and length of the vectors will be graded. The location of the vectors will not be graded. ANSWER:


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Problem 1.11 Description: (a) Figure shows two dots of a motion diagram and vector v_vec_2. Draw the vector v_vec_3 if the acceleration vector a_vec at dot 3 points to the right. (b) Figure shows two dots of a motion diagram and vector v_vec_2. Draw the vector v_vec_3 if...

Part A ⃗ at dot 3 Figure shows two dots of a motion diagram and vector v2⃗ . Draw the vector v3⃗ if the acceleration vector a

points to the right. Draw the vector with its tail at the dot 3. The orientation of your vector will be graded. The exact length of your vector will not be graded but the relative length of one to the other will be graded. ANSWER:


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Part B ⃗ at dot 3 Figure shows two dots of a motion diagram and vector v2⃗ . Draw the vector v3⃗ if the acceleration vector a

points to the left. Draw the vector with its tail at the dot 3. The orientation of your vector will be graded. The exact length of your vector will not be graded but the relative length of one to the other will be graded. ANSWER:


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Enhanced EOC: Problem 1.18 Description: The figure shows the motion diagram of a drag racer. The camera took one frame every 2 s. You may want to review Motion in One Dimension . For help with math skills, y ou may want to review: Plotting Points on a Graph (a) Make a... The figure shows the motion diagram of a drag racer. The camera took one frame every 2 s. You may want to review (

pages 16 - 19) .

For help with math skills, you may want to review: Plotting Points on a Graph


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Part A Make a position-versus-time graph for the drag racer.

Hint 1. How to approach the problem Based on Table 1.1 in the book/e-text, what two observables are associated with each point? Which position or point of the drag racer occurs first? Which position occurs last? If you label the first point as happening at the last position point occur?

t = 0 s, at what time does the next point occur? At what time does

What is the position of a point halfway in between x estimate the positions of the points using a ruler?

= 0 m and x = 200 m? Can you think of a way to

ANSWER:

Tactics Box 1.5 Drawing a Pictorial Representation Description: Knight Tactics Box 1.5 Drawing a Pictorial Representation is illustrated. (vector applet) (sorting applet) Learning Goal: To practice Tactics Box 1.5 Drawing a Pictorial Representation.


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You will find that motion problems and other physics problems often have several variables and other pieces of information to keep track of. The best w ay to tackle such problems is to draw a pictorial representation of the problem that shows all of the important details. This Tactics Box explains how to draw a pictorial representation of a motion problem.

TACTICS BOX 1.5 Drawing a pictorial representation

1. Draw a motion diagram. The motion diagram develops your intuition for the motion and, especially important, determines whether the signs of v and a are positive or negative. 2. Establish a coordinate system. Select your axes and origin to match the motion. For one-dimensional motion, you want either the x axis or the y axis parallel to the motion. 3. Sketch the situation. Not just any sketch. Show the object at the beginning of the motion, at the end , and at any point where the character of the motion c hanges. Show the object, not just a dot, but very simple drawings are adequate. 4. Define symbols. Use the sketch to define symbols representing quantities such as position, velocity, acceleration, and time. Every variable used later in the mathematical solution s hould be defined on the sketch. Some will have known v alues, and others are initially unknown, but all should be given symbolic names. 5. List known information. Make a table of the quantities whose values you can determine from the problem statement or that can be found quickly w ith simple geometry or unit conversions. Some quantities are implied by the problem, rather than explicitly given. Others are determined by your choice of coordinate system. 6. Identify the desired unknowns. What quantity or quantities will allow you to answer the question? These should have been defined as symbols in step 4. Don’t list every unknown, only the one or two needed to answer the question. Follow the steps above to draw a pictorial representation of the following problem: A light train is traveling on a straight section of track at a constant speed of 15 m/s. As it approaches the next station, it starts to slow down at a rate of 5 m/s2 until it stops at the station. From the moment the train starts to slow down, how long does it take for the train to reach the station? Note that you are not expected to solve this problem, only to draw the pictorial representation.

Part A Draw a motion diagram for the train. Assume that the train is moving toward the right and s tarts to slow down at t = 0 . The separation of each dot represents an elapsed time of one s econd. Include velocity vectors and the acceleration vector in your drawing. Keep in mind that the acceleration of the train has a magnitude of 5

m/s2 .

The orientation and length of the velocity vectors will be graded. Only the direction of the acceleration vector will be graded. The location of the vectors will not be graded.

Hint 1. How to draw the vectors with correct lengths Draw each velocity vector between the c orresponding two black dots. To draw the acceleration with the correct length, click on the vector info button; adjust the vector until the length displayed in the properties window has the desired value.

ANSWER:


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Part B Draw the coordinate system that is most appropriate for the train's motion. Since this problem deals with onedimensional motion, you need only the x -axis. Note that x i , x f , ti , tf , (vx ) i and (v x ) f are the initial position, final position, initial time, final time, initial velocity, and final velocity of the train, respectively. The orientation of the vector will be graded. The location and length of the vector will not be graded. ANSWER:


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Keep in mind that the choice of coordinate system is arbitrary. However, in problems involving one-dimensional motion it is often convenient to s elect the x -axis to match the motion. Thus, in this case the positive end of the x -axis is chosen to be to the right. It is also convenient in this problem to place the origin at t he location where the train starts to slow down.

Part C To complete your pictorial representation of the problem, you should compile two lis ts: one of known quantities and one of the unknown quantities that will allow you to answer the question in the problem. Below are all of the relevant quantities in this problem. Sort them accordingly. Drag the appropriate items to their respective bins. ANSWER:


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Now that you have identified the list of known and unknown quantities, you can add this information to your pictorial representation in the form of a table. The actual sketc h that you draw might look like this:

Made to Order (of Magnitude) Description: Several unrelated order-of-magnitude calculations. http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2736256

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Learning Goal: To be able to make order-of-magnitude calculations. Imagine that a company wants to build a new factory. Such a complex project would involve significant investment in terms of both time and money. Consequently, before construction can start the company asks for an estimate of the total cost. Although estimate figures are not exact, they are still helpful: For instance, if the projected cost is three times the amount of money that the company is w illing to spend, the project will be c anceled or substantially changed. Individuals make such estimates all the t ime. For instance, when you need to drive somewhere for a meeting, you can roughly predict how much time you will spend on the road and depart accordingly. Of course, the actual travel time is unlikely to be exactly the s ame as the estimated one—but it still helps to make an estimate so that you can decide when to leave. Physicists must frequently make such estimates—known as order-of-magnitude calculations—as part of their job. Depending on the results of the estimate, a potentially lengthy and costly research project may be postponed, canceled, or redesigned. Being able to make a quick calculation and get a "ball-park figure" of the expected result is an important skill for a scientist, involving processes such as identifying relevant information, searching for this information, and using your experience or background knowledge. In this problem, you will practice making such order-of-magnitude calculations.

What is the total mass of all the people on earth? It is impossible, of course, to give an accurate answer to this question. However, it is quite possible to find the order of magnitude of the answer. All one needs to do is to use some common sense and, possibly, search for relevant reference information. The calculation can proceed as follows: There are about 7 × 109 people on earth. An average adult male weighs, say, 75 kg; an average adult female weighs about 60 kg , and an average child will weigh considerably less than 60 kg. Figuring roughly one child per adult, we can reasonably say that an average person's mass is about 50 kg, which gives the total mass of all humans on our planet as

7 × 109

× 50

= 3.5 × 1011 kg .

Of course, we may be off in our estimates of the average mass or number of people. While it would be unreasonable to say that we know the total mass is 3.5 × 1011 kg , we can be reasonably sure that we have the correct order of magnitude; that is, we have the correct exponent to which the number 10 is raised. In each of the following problems, you will be asked to make similar estimates.

Part A How many people can fit into the Pentagon, which was once the largest office building in t he world? Assume that everybody must be standing on the floor. Round the answer to the nearest power of 10 and then express your answer as the order of magnitude. For instance, if your estimated answer is 3 × 105 , enter 5. If your estimated answer is 8.7 × 105, you should enter 6 (rounding up to the next power of 10).

Hint 1. What reference information should you be looking for? What information should you be looking for?


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Check all that apply. ANSWER: What is the tallest building in t he world? What is the most massive building in the world? What building in the world has the largest floor area? In which country is the largest building in the world located? How many people can be found in the largest building in t he world on a typical day?

Only the floor area matters here; height, mass, and location are irrelevant. The number of people working in the building on a typical day probably does not matter: One would hope that, on a normal day, this building is not "standing room only."

Hint 2. What numeric quantities do you need to estimate? What numeric quantities do you need to estimate? Check all that apply. ANSWER: the mass of an average person the height of an average person the amount of space the average person needs to work efficiently the the area that an average person takes up while standing the volume of an average person

ANSWER: 6

Your process for solving this problem might have been something like this: First, a simple library or Internet search would tell you that the largest building in the world (in terms of the total floor area) is the Pentagon, the main building of the U.S. Department of Defense. Its total floor area is about

6.5 × 106 ft 2

3.8 × 106 ft 2 can be occupied; it would be hard to stand inside a wall! Assuming that an average person occupies about 2.0 ft 2 when standing (a conservative estimate), we can see that about 1.9 × 106 people (more than three times the entire population of Washington, DC) could fit into the Pentagon but only

—assuming the floors held up! Your own answer may have been different from ours or used different details; however, the order of magnitude was, hopefully, the same.


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Part B If the entire population of the United States forms a human chain by holding hands, how many times can such a chain be wrapped around the earth's equator? Round your answer to the nearest integer. ANSWER: 7 Also accepted: 5, 6, 8, 9, 10, 11, 12, 13, 14, 15

Here is one way to solve this problem: There are about 300 million people in the United States. The distance between the tips of a person's outstretched hands is roughly equal to the height of the person. C ounting children, we estimate the average palm-to-palm distance as one meter. Since the equator is about 40 million meters long, division yields about 7.5. However, in this part any answer between 5 and 15 is considered correct—after all, we are just estimating .

Part C How many times does your heart beat during your lifetime? Round the answer to the nearest power of 10 and then express your answer as the order of magnitude. For instance, if your estimated answer is 3 × 105 , enter 5. If your estimated answer is 8.7 × 105, you should enter 6 (rounding up to the next power of 10). ANSWER: 9

On average, your heart beats about once every second. The number of seconds in t he lifetime of an average U.S. resident is

86,400

s × 365 days × 75 years year day lifetime

= 2.4 × 109 s

assuming a lifetime of 75 years. Of course, we didn't account for leap years since this is just an estimate.

Part D Legend has it that, many centuries ago, Archimedes jumped out of his bathtub and ran across town naked screaming "Eureka!" after he solved an especially difficult problem. Though you may not have thought of things this way before, when you drink a glass of water, the water that you are drinking contains some water molecules that were in Archimedes' bathwater that day, because water doesn't get created or destroyed on a large scale. It follows the water cycle, which includes rain, evaporation, flowing of rivers into the ocean, and so on. In the more than two thousand years since his discovery, the water molecules from Archimedes' bathwater have been through this cycle enough times that they are probably about evenly distributed throughout all the water on the earth. When you buy a can of soda, about how many molecules from that famous bathtub of Archimedes are there in that can?


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Round the answer to the nearest power of 10 and then express your answer as the order of magnitude. For instance, if your estimated answer is 3 × 105 , enter 5. If your estimated answer is 8.7 × 105, you should enter 6 (rounding up to the next power of 10).

Hint 1. How to approach the problem Assume that the water from that bathtub is evenly mixed with the water throughout the surface of the Earth-after all, it has had more than 2000 years to do so.

Hint 2. Avogadro's number

6.0 × 1023 molecules in 18 g of water; in other words, 1 kg of water contains about 3.3 × 1025 molecules . There are about

Hint 3. What to estimate Estimate the mass of water in Archimedes' bathtub and the total mass of water on earth. (Note that most of the earth's water is in its oceans.)

ANSWER: 6 Also accepted: 7, 5

We used the following assumptions: The total mass of water on the earth's surface is

1.4 × 1021 kg (reference

information available from many different sources); the mass of the water in the bathtub is guessed to be 200 kg ; the mass of the water in the can of soda is estimated to be about 0.33 kg; and 1 kg of water contains about 3.3 × 1025

molecules.

Thus the total number of molecules in the can is roughly

1025. The fraction of the bathtub molecules in the can

is 200/(1.4 × 1021 ) . Therefore, the number of bathtub molecules contained in the can is

200× 1025 ≈ 1.4×1021

1.4 × 106 .

Your answer is most likely different but it should still have the same order of magnitude, equal to 6. In case of some "wilder" assumptions, we count 5 and 7 as correct too.

Converting between Different Units Description: Problems in unit conversion: one based importing goods and another on the Mars Climate Orbiter . Unit conversion problems can seem tedious and unnecessary at times. However, different systems of units are used in different parts of the world, so when dealing with international transactions, documents, s oftware, etc., unit conversions are often necessary.


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Here is a simple example. The inhabitants of a small island begin exporting beautiful cloth made from a rare plant that grows only on their island. Seeing how popular the small quantity that they export has been, they steadily raise their prices. A clothing maker from New York, thinking that he can save money by "cutting out the middleman," decides to travel to the small island and buy t he cloth himself. Ignorant of the local c ustom of offering strangers outrageous prices and then negotiating down, the clothing maker accepts (much to everyone's surpise) the initial price of 400 tepizes/m 2. 2

The price of this cloth in New York is 120 dollars/yard .

Part A If the clothing maker bought 500

m2

of this fabric, how much money did he lose? Use

1 tepiz = 0.625 dollar and

0.9144 m = 1 yard. Express your answer in dollars using two significant figures.

Hint 1. How to approach the problem To find how much money the clothing maker loses, you must find how much money he spent and how much he would have spent in New York. Furthermore, since the problem asks how much he lost in dollars, you need to determine both in dollars. This will require unit conversions.

Hint 2. Find how much he paid If the clothing maker bought 500

m 2 at a cost of 400 tepizes/m 2 , then simple multiplication will give how

much he spent in tepizes. Once you've f ound that, convert to dollars. How much did the clothing maker spend in dollars? Express your answer in dollars to three significant figures.

Hint 1. Find how much he paid in If the clothing maker bought 500 in

tepizes

m 2 at a cost of 400 tepizes/m 2 , then how much did he pay in total,

tepizes ?

Express your answer in

tepizes.

ANSWER: 2.00!105

tepizes

ANSWER: 1.25!105

dollars

Hint 3. Find the price in New York You know that the price of the fabric in New York is 120

dollars/yard2 . Thus, you need only to find the


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number of square yards that the clothing maker purchased and then multiply to find the price in New York. What would it have cost him to buy the fabric in New York? Express your answer in dollars to three significant figures.

Hint 1. Determine how much cloth he bought in yard

2

0.9144 m = 1 yard. Squaring both sides, you would get that 0.8361 m 2 = 1 yard2 . How much is 500 m 2 ? You are given that

Express your answer in

yard2 to three significant figures.

ANSWER: 598

yard2

ANSWER: 7.18!104

dollars

ANSWER: 5.3!104

dollars

Still think that unit conversion isn't important? Here is a widely publicized, true st ory about how failing to convert units resulted in a huge loss. In 1998, the Mars Climate Orbiter probe crashed into the surface of Mars, instead of entering orbit. The resulting inquiry revealed that NASA navigators had been making minor course corrections in SI units, whereas the software written by the probe's makers implicitly used British units. In the United States, most scientists use SI units, whereas most engineers use the British, or Imperial, system of units. (Interestingly, British units are not used in Britain.) For these two groups to be able to communicate to one another, unit conversions are necessary. The unit of force in the SI system is the newton (N), which is defined in terms of basic SI units as 1 N = 1 kg ⋅ m/s 2 . The unit of force in the British system is the pound (lb ), which is defined in terms of the slug (British unit of mass), foot ( ft ), and second (s) as 1 lb = 1 slug ⋅ ft/s 2 .

Part B Find the value of 15.0

N in pounds. Use the conversions 1 slug = 14.59 kg and 1 ft = 0.3048 m.

Express your answer in pounds to three significant figures.

Hint 1. How to approach the problem


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When doing a unit conversion, you should begin by comparing the units you are starting with and the units you need to finish with. In this problem, we have the following: Starting unitsFinal units

kg⋅m s2

slug⋅ft s2

Notice that both have seconds squared in the denominator. You will only have to change the units in the numerator. Match up the units that measure the same quantity (e.g., kilograms and slugs both measure mass). Once you've done this, create a fraction (e.g., 1 hour/60 minutes) based on conversion factors such that the old unit is canceled out of the expression and the new unit appears in the position (i.e., numerator or denominator) of the old unit. In this problem, there are two pairs wit hin the starting and final units that must be converted in this way (i.e., kilograms/slugs and meters/feet).

Hint 2. Calculate the first conversion The first step is to eliminate kilograms from the expression for newtons in favor of slugs. What is the value of 15 kg ⋅ m/s2 in slug ⋅ m/s2 ? Express your answer in slug-meters per second squared to four significant figures. ANSWER: 1.028

Follow the same procedure to replace meters with feet.

ANSWER: 15.0 N = 3.37

lb

Thus, if the NASA navigators believed that they were entering a force value of 15 N (3.37 lb), they were actually entering a value nearly four and a half times higher, 15 lb. Though these errors were only in tiny course corrections, they added up during the trip of many millions of kilometers. In the end, the blame for the loss of the 125-million-dollar probe was placed on the lack of communication between people at NASA that allowed the units mismatch to go unnoticed. Nonetheless, this story makes apparent how important it is to carefully label the units used to measure a number.

Consistency of Units Description: Short quantitative problem on dimensional analysis. Requires that students manipulate physics equations to find the units of certain unknown quantities. This problem is based on Young/Geller Quantitative Analysis 1.3 In physics, every physical quantity is measured with respect to a unit . Time is measured in seconds, length is measured in meters, and mass is measured in kilograms. K nowing the units of physical quantities will help you solve problems in physics. http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2736256

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Part A Gravity causes objects to be attracted to one another. This attraction keeps our feet firmly planted on the ground and causes the moon to orbit the earth. The f orce of gravitational attraction is represented by the equation Gm1m 2 , F = r2 where F is the magnitude of the gravitational attraction on either body, m 1 and m 2 are the masses of the bodies, r

G is the gravitational constant. In SI units, the units of force are kg ⋅ m/s 2 , the units of mass are kg, and the units of distance are m. For this equation to have consistent units, the units of G is the distance between them, and must be which of the following?

Hint 1. How to approach the problem To solve this problem, we start with the equation Gm1m 2 . r2 For each symbol whose units we k now, we replace the symbol with those units. For example, we replace

F =

with

m1

kg. We now solve this equation for G .

ANSWER:

kg 3 m⋅s 2 kg⋅s 2 m3 m3 kg⋅s 2 m kg⋅s 2

Part B One consequence of Einstein's theory of special relativity i s that mass is a form of energy. This mass-energy relationship is perhaps the most famous of all physic s equations: E = mc2 ,

c is the speed of the light, and E is the energy. In SI units, the units of speed are m/s. For the preceding equation to have consistent units (the same units on both sides of the equation), the units of E must be where m is mass,

which of the following?

Hint 1. How to approach the problem To solve this problem, we start with the equation

E = mc2 . For each symbol whose units we k now, we replace the symbol with those units. For example, we replace


m Page 21 of 26


with

g. We now solve this equation for

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.

ANSWER:

kg⋅m s kg⋅m2 s2 kg⋅s 2 m2 kg⋅m2 s

To solve the types of problems typified by these examples, we start with the given equation. For each symbol whose units we know, we replace the symbol with those units. For example, we replace m with kg . We now solve this equation for the units of the unknown variable.

Problem 1.23 Description: Convert the following to SI units: (a) v1... (b) v2... (c) v3... (d) v4... Convert the following to SI units:

Part A 5.35ms ANSWER: = 5.35!10 3 "

Part B 135 km/h ANSWER: = 37.5

Part C


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37.1

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m

ANSWER: = 3.71!104

Part D 47µm/ms ANSWER: = 4.70!10 2 "

Problem 1.25 Description: Convert the following to SI units: (a) dc hours... (b) vc days.. . (c) ac year... (d) bc (ft)/s... Convert the following to SI units:

Part A 3.00 hours Express your answer with the appropriate units. ANSWER: = 1!104

Part B 2.00 days Express your answer with the appropriate units. ANSWER: = 2!105

Part C 1.00 year


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Express your answer with the appropriate units. ANSWER: = 3!107

Part D 249 ft/s Express your answer with the appropriate units. ANSWER: = 75.9

Problem 1.27 Description: Using the approximate conversion factors in table below, convert the following SI units to English without using your calculator. Approximate conversion factors 10 cm approx 4 in 1 m approx 1 yard 1 m approx 3 feet ... Using the approximate conversion factors in table below, convert the following SI units to English without using your calculator. Approximate conversion factors

10 cm ≈ 4 in 1 m ≈ 1 yard 1 m ≈ 3 feet 1 km ≈ 0.6 mile 1 m/s ≈ 2 mph Part A 20cm Express your answer to two significant figures. ANSWER: = 8.0 inches

Part B 20m/s http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2736256

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Express your answer to two significant figures. ANSWER: = 40 mph

Part C 5km Express your answer to one significant figure. ANSWER: = 3 miles

Part D 0.7cm Express your answer to two significant figures. ANSWER: = 0.28 inches

Enhanced EOC: Problem 1.54 Description: The quantity called mass density is the mass per unit volume of a s ubstance. Express the following mass densities in SI units.You may want to review Unit and Significant Figures . For help with math skills, you may want to review: Conversio... The quantity called mass density is the mass per unit volume of a substance. Express the f ollowing mass densities in SI units. You may want to review (

pages 23 - 27) .

For help with math skills, you may want to review: Conversion Between m and cm Conversion Between mg, g, kg

Part A Silver,

10.5 × 10−3 kg/cm 3


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Express your answer with the appropriate units.

Hint 1. How to approach the problem What are the units of mass density in SI units? How many centimeters are in a meter? How do you convert from

1/cm to 1/m ?

How do you convert from

1/cm 3

to 1/m 3 ?

ANSWER: = 1.05!104

Part B Alcohol,

0.81 g/cm3

Express your answer with the appropriate units.

Hint 1. How to approach the problem How many grams are in a kilogram? How do you convert from grams to kilograms?

ANSWER: = 810

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Ch 1 HW Solutions

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