Q: A student measures the length and width of a rectangle as $$l = (8.90 \pm 0.05)\ \text{cm}$$ and $$w = (5.65 \pm 0.05)\ \text{cm}. $$What is the best estimate for the perimeter?

$$P_{\text{best}} = 2(8.90\ \text{cm} + 5.65\ \text{cm}) = 29.10\ \text{cm}$$

Q: Given $$l = (8.90 \pm 0.05)\ \text{cm}$$ and $$w = (5.65 \pm 0.05)\ \text{cm}$$, what is the uncertainty in the perimeter $$P = 2l + 2w$$?

$$\delta P = 2(0.05\ \text{cm}) + 2(0.05\ \text{cm}) = 0.20\ \text{cm}$$

Q: A cylindrical piece of metal has mass $$m = (5.0 \pm 0.2)\ \text{kg}$$ and volume $$V = (20.2 \pm 0.5)\ \text{m}^3. $$What is the density, properly expressed with uncertainty?

$$(0.25 \pm 0.02)\ \text{kg/m}^3$$

Q: If the area of a rectangle is calculated as $$A = l \times w$$ with $$l = (8.90 \pm 0.05)\ \text{cm}$$ and $$w = (5.65 \pm 0.05)\ \text{cm}$$, what is the best estimate and uncertainty for the area?

$$(50.3 \pm 0.7)\ \text{cm}^2$$

Q: Which of the following is the correct expression for the relative uncertainty in the area $$A of a $$rectangle with $$l$$ and $$w$$ measured with uncertainties?

$$\frac{\delta A}{A_{\text{best}}} = \frac{\delta l}{l} + \frac{\delta w}{w}$$

Question 1

Which of the following best describes the primary focus of physics as a science?

Accepted Answer

The study of the laws that determine the structure of the universe, focusing on matter and energy and their interrelationships.

Question 2

Which of the following is a correct example of a physical quantity and its SI base unit?

Accepted Answer

Mass - kilogram (kg)

Question 3

A student measures the length and width of a rectangle as $$l = (8.90 \pm 0.05)\ 	ext{cm}$$ and $$w = (5.65 \pm 0.05)\ 	ext{cm}. $$What is the best estimate for the perimeter?

Accepted Answer

$$P_{	ext{best}} = 2(8.90\ 	ext{cm} + 5.65\ 	ext{cm}) = 29.10\ 	ext{cm}$$

Question 4

Given $$l = (8.90 \pm 0.05)\ 	ext{cm}$$ and $$w = (5.65 \pm 0.05)\ 	ext{cm}$$, what is the uncertainty in the perimeter $$P = 2l + 2w$$?

Accepted Answer

$$\delta P = 2(0.05\ 	ext{cm}) + 2(0.05\ 	ext{cm}) = 0.20\ 	ext{cm}$$

Question 5

Which of the following equations is dimensionally correct for velocity $$v$$, acceleration $$a$$, and time $$t$$?

Accepted Answer

$$v = at$$

Question 6

A cylindrical piece of metal has mass $$m = (5.0 \pm 0.2)\ 	ext{kg}$$ and volume $$V = (20.2 \pm 0.5)\ 	ext{m}^3. $$What is the density, properly expressed with uncertainty?

Accepted Answer

$$(0.25 \pm 0.02)\ 	ext{kg/m}^3$$

Question 7

Which of the following numbers has the most significant figures?

Accepted Answer

0.0123400

Question 8

Which of the following numbers has the highest precision?

Accepted Answer

5.1762394 	imes $$10^8$$

Question 9

Which is the proper way to express $$1234.67 in $$scientific notation?

Accepted Answer

$$1.23467 	imes 10^3$

Question 10

Which of the following is the correct SI unit and dimension for force?

Accepted Answer

Newton (N), $$MLT^{-2}$$

Question 11

If the area of a rectangle is calculated as $$A = l 	imes w$$ with $$l = (8.90 \pm 0.05)\ 	ext{cm}$$ and $$w = (5.65 \pm 0.05)\ 	ext{cm}$$, what is the best estimate and uncertainty for the area?

Accepted Answer

$$(50.3 \pm 0.7)\ 	ext{cm}^2$$

Question 12

Which statement about uncertainty in measurement is correct?

Accepted Answer

Uncertainty should be quoted to one significant figure.

Question 13

Which of the following is a correct rule for propagation of uncertainties when adding two measured quantities $$A$$ and $$B$$?

Accepted Answer

$$\delta C = \delta A + \delta B$$ for $$C = A + B$$

Question 14

Which of the following is the correct expression for the relative uncertainty in the area $$A of a $$rectangle with $$l$$ and $$w$$ measured with uncertainties?

Accepted Answer

$$\frac{\delta A}{A_{	ext{best}}} = \frac{\delta l}{l} + \frac{\delta w}{w}$$

Question 15

Why must all physical relationships (equations) be dimensionally correct?

Accepted Answer

To ensure that the units on both sides of the equation are consistent and meaningful.

Question 16

A car travels at 50 mph. What is its speed in SI units (m/s)? (1 mile = 1609 m, 1 hour = 3600 s)

Accepted Answer

22 m/s

Question 17

The volume of a sphere is $$23\ 	ext{cm}^3. $$What is the radius in feet? (1 foot = 30.48 cm)

Accepted Answer

0.058 ft

Question 18

Which of the following best describes the role of physics in life sciences?

Accepted Answer

Physics provides quantitative models and explanations for biological phenomena at the biomolecular level.

Physics 1210: Introduction, Physical Quantities, and Measurement Uncertainties

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