Question 1

Order-of-magnitude estimates are useful in physics because they allow us to:

Accepted Answer

Get a rough sense of the scale of a problem before detailed calculations.

Question 2

Which formula would you use to estimate the volume of the Earth, assuming it is a sphere?

Accepted Answer

$$V = \frac{4}{3}\pi R^3$

Question 3

If the average density of rock is $$5 	imes 10^3$ kg/m^3$ and the Earth's volume is 1.1$$ 	imes $$10^{21} m$^3$$, what is the order-of-magnitude estimate for the Earth's mass?

Accepted Answer

$$5 	imes 10$$^{24}$$ kg

Question 4

Why can the mass of the ocean be ignored in an order-of-magnitude estimate of Earth's mass?

Accepted Answer

Because the ocean's mass is negligible compared to the mass of the rocks.

Question 5

Superman flies around the Earth 7.5 times per second at nearly the speed of light. If the speed of light is $$3 	imes 10^8$ m/s, what is the approximate circumference of the Earth?

Accepted Answer

$$6.4 	imes 10^6$ m

Question 6

Given the Earth's radius $$R_E \approx 6.4 	imes 10^6$ m, what is the order-of-magnitude estimate for Earth's volume?

Accepted Answer

$$1.1 	imes 10$$^{21}$$ m^3$

Question 7

Which of the following best describes an order-of-magnitude estimate?

Accepted Answer

A rough estimate, usually within a factor of 10.

Question 8

If you double the radius of a sphere, by what factor does its volume increase?

Accepted Answer

By a factor of 8

Question 9

Which of the following is the correct formula for the density of a material?

Accepted Answer

$$\rho = \frac{m}{V}$$

Question 10

A physicist wants to estimate the mass of Mars using the same method as for Earth. If Mars has a radius about half that of Earth and the same average density, what is the order-of-magnitude estimate for Mars' mass compared to Earth's?

Accepted Answer

About 1/8 of Earth's mass

Question 11

Which of the following is NOT a reason to use order-of-magnitude estimates in physics?

Accepted Answer

To replace all experimental measurements.

Question 12

If the density of rock is $$5 	imes 10^3$ kg/m^3$ and the radius of Earth is 6.4$$ 	imes $$10^6 m$$, what is the formula for the mass of Earth?

Accepted Answer

$$m = \rho \frac{4}{3}\pi R^3$

Question 13

Which of the following best describes the process of making a ballpark estimate?

Accepted Answer

Using reasonable approximations to estimate a value within an order of magnitude.

Question 14

If the measured mass of Earth is $$6 	imes 10$$^{24}$$ kg and your estimate is 5$$ 	imes $$10^{24} kg$$, what does this tell you about your estimation method?

Accepted Answer

The estimation method gives a reasonable approximation.

Order-of-Magnitude Estimation in Physics: Estimating Earth's Mass

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