# Mastering Physics Homework 1 Solutions

11/3/13 Homework 1session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2469924 1/59

Homework 1

Due: 5:00pm on Sunday, September 1, 2013

You will receive no credit for items you complete after the assignment is due. Grading Policy

Converting Units

The ability to convert from one system of units to another is important in physics. It is often impractical to measure quantities in the standard meters,kilograms, and seconds, but the laws of physics that you learn will involve constants that are defined in these units. Therefore, you may often have toconvert your measured quantities into meters, kilograms, and seconds.The following table lists metric prefixes that come up frequently in physics. Learning these prefixes will help you in the various exercises.mega- ()kilo- ()centi- ()milli- ()micro- ()nano- ()When doing unit conversions, you need a relation between the two units. For instance, in converting from millimeters to meters, you need to know that.Once you know this, you need to divide one side by the other to obtain a ratio of to :.If you are converting from millimeters to meters, then this is the proper ratio. It has in the denominator, so that it will cancel the units of the quantitythat you are converting. For instance, if you were converting , then you would have.If you were converting a quantity from meters to millimeters, you would use the reciprocal ratio:.

Part A

Suppose that you measure a pen to be 10.5 long. Convert this to meters.

Express your answer in meters.

Hint 1.

Relating centimeters and meters

To solve this problem, you will need to use the relation . You can determine such relations using the metric prefixes given in theintroduction to this problem. If one centimeter equals meters, then you need centimeters to equal a whole meter, just as you knowthat if one quarter equals US dollars, then you need quarters to equal a whole US dollar. ANSWER:

Correct

When converting areas, you must be careful to use the correct ratio. If you were converting from to , it might be tempting to useagain. Be careful! Think of as . That is to say, think of this as a pair of millimeter units, each of which must be convertedseparately. To convert to square meters you would use the following calculation:.

M ×10

6

k ×10

3

c ×10

−2

m ×10

−3

μ

×10

−6

n ×10

−9

1m=1000mm mmm

1=

1m 1000mm

mm 63mm

63⋅=0.063m mm

1m 1000mm

1=

1000mm 1m

cm 100cm=1m 10

−2

10

2

4

−1

4

1

10.5 = 0.105

cmm mm

2

m

2

1m 1000mm

mm

2

(mm=(mm)⋅(mm) )

2

130mm

2

130m⋅

(

⋅

(

=130m⋅ m

2 1m 1000mm 1m 1000mm

m

2

(

1m mm 10

3

2

Ch 1Due: 11:59pm on Wednesday, January 27, 2016You will receive no credit for items you complete after the assignment is due. Grading PolicyPrelecture Concept Question 1.11Part AIn the study of physics, what distinguishes a scalar from a vector?ANSWER:CorrectExercise 1.5The most powerful engine available for the classic 1963 Chevrolet Corvette Sting Ray developed 360 horsepower and had adisplacement of 327 cubic inches.Part AExpress this displacement in liters () by using only the conversions and .ANSWER:CorrectProblem 1.16Express each of the following approximations of to six significant figures.Part AExpress your answer using six significant figures.ANSWER:A scalar is a dimensionless number, while vectors are numbers that have dimensions.Scalars have both a magnitude and a direction, but vectors have only a magnitude.Nothing—the terms “vector” and “scalar” are different names for the same thing.A scalar is specified with a single number, but a vector is specified using both a magnitude and a direction.A scalar must always be positive, but vectors can be positive, negative, or zero.L1 L = 1000 cm31 in = 2.54 cm5.36 Lπ

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