Cap1

Chapter 1 Measurement and Vectors
Conceptual Problems
1 • [SSM] Which of the following is not one of the base quantities in the SI system? (a) mass, (b) length, (c) energy, (d) time, (e) All of the above are base quantities.

Determine the Concept The base quantities in the SI system include mass, length, and time. Force is not a base quantity. (c) is correct.
2

In doing a calculation,you end up with m/s in the numerator and m/s2 in the denominator. What are your final units? (a) m2/s3, (b) 1/s, (c) s3/m2, (d) s, (e) m/s.
•

Picture the Problem We can express and simplify the ratio of m/s to m/s2 to determine the final units. Express and simplify the ratio of m/s to m/s2: m 2 s = m ⋅ s = s and (d ) is correct. m m ⋅s 2 s

3

•

The prefix giga means (a) 103, (b) 106, (c)109, (d) 1012, (e) 1015.

Determine the Concept Consulting Table 1-1 we note that the prefix giga means 109. (c) is correct.
4 •

The prefix mega means (a) 10–9, (b) 10–6, (c) 10–3, (d) 106, (e) 109.

Determine the Concept Consulting Table 1-1 we note that the prefix mega means 106. (d ) is correct. [SSM] Show that there are 30.48 cm per foot. How many centimeters are there in one mile?
5•

Picture the Problem We can use the facts that there are 2.540 centimeters in 1 inch and 12 inches in 1 foot to show that there are 30.48 cm per ft. We can then use the fact that there are 5280 feet in 1 mile to find the number of centimeters in one mile.

1

2

Chapter 1

Multiply 2.540 cm/in by 12 in/ft to find the number of cm per ft:

cm ⎞ ⎛ in ⎞ ⎛ ⎜ 2.540 ⎟ ⎜12 ⎟ = 30.48 cm/ftin ⎠ ⎝ ft ⎠ ⎝

Multiply 30.48 cm/ft by 5280 ft/mi to find the number of centimeters in one mile: ft ⎞ cm ⎞ ⎛ ⎛ 5 ⎜ 30.48 ⎟ ⎜ 5280 ⎟ = 1.609 × 10 cm/mi mi ⎠ ft ⎠ ⎝ ⎝
Remarks: Because there are exactly 2.54 cm in 1 in and exactly 12 inches in 1 ft, we are justified in reporting four significant figures in these results. 6

The number 0.000 513 0 has • (c) four, (d) seven, (e) eight.significant figures. (a) one, (b) three,

Determine the Concept Counting from left to right and ignoring zeros to the left of the first nonzero digit, the last significant figure is the first digit that is in doubt. Applying this criterion, the three zeros after the decimal point are not significant figures, but the last zero is significant. Hence, there are four significant figures in this number. (c)is correct.

The number 23.0040 has (c) four, (d) five, (e) six.
7 •

significant figures. (a) two, (b) three,

Determine the Concept Counting from left to right, the last significant figure is the first digit that is in doubt. Applying this criterion, there are six significant figures in this number. (e) is correct. 8 • Force has dimensions of mass times acceleration. Acceleration hasdimensions of speed divided by time. Pressure is defined as force divided by area. What are the dimensions of pressure? Express pressure in terms of the SI base units kilogram, meter and second. Determine the Concept We can use the definitions of force and pressure, together with the dimensions of mass, acceleration, and length, to find the dimensions of pressure. We can express pressure in terms ofthe SI base units by substituting the base units for mass, acceleration, and length in the definition of pressure.

Measurement and Vectors Use the definition of pressure and the dimensions of force and area to obtain: Express pressure in terms of the SI base units to obtain:
ML 2 [P] = [F ] = T 2 = M 2 [A] L LT m kg ⋅ 2 N s = kg = 2 2 m m m ⋅ s2

3

9

• True or false: Two quantitiesmust have the same dimensions in order to be multiplied.

False. For example, the distance traveled by an object is the product of its speed (length/time) multiplied by its time of travel (time).
10 • A vector has a negative x component and a positive y component. Its angle measured counterclockwise from the positive x axis is (a) between zero and 90 degrees. (b) between 90 and 180 degrees. (c)...