Q: A student estimates the walking speed of a typical college student to be $$1.5 \ \mathrm{m/s}. $$The actual measured value is $$1.3 \ \mathrm{m/s}. $$What is the percent difference between the estimate and the measured value?

$$\displaystyle \frac{1.5 - 1.3}{1.3} \times 100\% = 15.4\%$$

Q: A group measures the time for a ball to fall $$2.00 \ \mathrm{m} as$$ $$0.64 \ \mathrm{s}. $$What is their measured acceleration due to gravity?

$$a = \displaystyle \frac{2 \times 2.00}{(0.64)^2$} = 9.77 \ \mathrm{m/s^2$}$$

Q: If the accepted value for $$g is$$ $$9.81 \ \mathrm{m/s^2$}$$ and your measured value is $$9.77 \ \mathrm{m/s^2$}$$, what is the percent difference?

$$\displaystyle \frac{|9.81 - 9.77|}{9.81} \times 100\% = 0.41\%$$

Question 1

A student measures the diameter of a metal sphere as $$4.00 \ \mathrm{cm}$$ with a ruler that has a precision of $$0.01 \ \mathrm{cm}. $$The mass of the sphere is measured as $$268.0 \ \mathrm{g}$$ with a balance that has a precision of $$0.1 \ \mathrm{g}. $$What is the density of the sphere in $$\mathrm{kg/m^3$}$$, and which measurement contributes more to the uncertainty in the density?

Accepted Answer

Density $$\approx 4010 \ \mathrm{kg/m^3$}$$; the diameter measurement contributes more to the uncertainty.

Question 2

You are asked to estimate the number of blades of grass on a football field. Which of the following is the best approach to make a reasonable estimate?

Accepted Answer

Count the number of blades in a small, known area, then multiply by the total area of the field.

Question 3

A student estimates the walking speed of a typical college student to be $$1.5 \ \mathrm{m/s}. $$The actual measured value is $$1.3 \ \mathrm{m/s}. $$What is the percent difference between the estimate and the measured value?

Accepted Answer

$$\displaystyle \frac{1.5 - 1.3}{1.3} 	imes 100\% = 15.4\%$$

Question 4

If you drop a ball from a height $$d$$ and measure the time $$t it $$takes to hit the ground, which formula should you use to calculate the acceleration due to gravity $$a$$?

Accepted Answer

$$a = \displaystyle \frac{2d}{t^2$}$$

Question 5

A group measures the time for a ball to fall $$2.00 \ \mathrm{m} as$$ $$0.64 \ \mathrm{s}. $$What is their measured acceleration due to gravity?

Accepted Answer

$$a = \displaystyle \frac{2 	imes 2.00}{(0.64)^2$} = 9.77 \ \mathrm{m/s^2$}$$

Question 6

Which of the following best describes the purpose of calculating percent difference in experimental physics?

Accepted Answer

To compare the accuracy of an experimental value to a known or accepted value.

Question 7

A student measures the time for a ball to fall from a height of $$1.80 \ \mathrm{m}$$ five times and gets: $$0.60, 0.62, 0.61, 0.63, 0.60$$ seconds. What is the average time?

Accepted Answer

$$0.612 \ \mathrm{s}$$

Question 8

If the accepted value for $$g is$$ $$9.81 \ \mathrm{m/s^2$}$$ and your measured value is $$9.77 \ \mathrm{m/s^2$}$$, what is the percent difference?

Accepted Answer

$$\displaystyle \frac{|9.81 - 9.77|}{9.81} 	imes 100\% = 0.41\%$$

Question 9

Which of the following is the most significant source of error when measuring the acceleration due to gravity by timing a falling ball?

Accepted Answer

Reaction time when starting and stopping the stopwatch.

Question 10

A student wants to improve the precision of their measurement of the density of a sphere. Which of the following should they do?

Accepted Answer

Take multiple measurements and use the average value.

Question 11

When estimating the walking speed of a student, which of the following is the best way to minimize random errors?

Accepted Answer

Repeat the measurement several times and average the results.

Question 12

If you measure a distance as $$5.0 \ \mathrm{m}$$ and the time to walk it as $$4.0 \ \mathrm{s}$$, what is the calculated walking speed?

Accepted Answer

$$1.25 \ \mathrm{m/s}$$

Question 13

A student estimates the number of blades of grass on Earth to be $$1 	imes 10$$^{18}$$, while an internet source gives 3$$ 	imes $$10^{18}. $$What is the percent difference?

Accepted Answer

$$\displaystyle \frac{|1 	imes 10$$^{18}$$ - 3 	imes 10$$^{18}$$|}{3 	imes 10$$^{18}$$} 	imes 100\% = 66.7\%$$

Question 14

Which of the following best describes the difference between precision and accuracy?

Accepted Answer

Precision refers to the repeatability of measurements; accuracy refers to how close a measurement is to the true value.

Question 15

If you want to estimate the number of cars passing a point on a highway in one hour, which method is most reliable?

Accepted Answer

Count the number of cars in one minute and multiply by 60.

Question 16

A student measures the time for a ball to fall from $$1.5 \ \mathrm{m} as$$ $$0.55 \ \mathrm{s}. $$What is the calculated acceleration due to gravity?

Accepted Answer

$$a = \displaystyle \frac{2 	imes 1.5}{(0.55)^2$} = 9.91 \ \mathrm{m/s^2$}$$

Question 17

Which of the following is NOT a good practice when making scientific measurements?

Accepted Answer

Rounding all measurements to the nearest whole number before calculations.

Question 18

If you are asked to estimate a quantity for which you have no direct data, what is the best strategy?

Accepted Answer

Break the problem into smaller, more familiar parts and estimate each part.

Precision Measurements, Estimation, and Acceleration in Introductory Physics

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