High School Physics : High School Physics

Study concepts, example questions & explanations for High School Physics

varsity tutors app store varsity tutors android store

Example Questions

Example Question #3 : Calibrations And Precision

Which of these is an example of high accuracy?

Possible Answers:

A student repeatedly calculates the mass of an object to be 49 grams, when the true mass is 52 grams

A student throws three pencils into the trash can, but misses and hits the window each time

An archer hits the bulls-eye

An archer hits the same spot on the target three times in a row

A student calculates the acceleration due to gravity to be \(\displaystyle 10.2\frac{m}{s^2}\) using three different methods

Correct answer:

An archer hits the bulls-eye

Explanation:

Accuracy is the measure of difference between a calculated value and the true value of a measurement. High accuracy demands that the experimental result be equal to the theoretical result.

In contrast, precision is a measure of reproducibility. If multiple trials produce the same result each time with minimal deviation, then the experiment has high precision. This is true even if the results are not true to the theoretical predictions; an experiment can have high precision with low accuracy.

An archer hitting a bulls-eye is an example of high accuracy, while an archer hitting the same spot on the bulls-eye three times would be an example of high precision.

Example Question #1 : Understanding Significant Figures

How many significant figures should be kept when multiplying \(\displaystyle 32.1kg*0.003\frac{m}{s^2}\)?

Possible Answers:

5

0

2

3

1

Correct answer:

3

Explanation:

Always keep the least number of significant figures. Two types of figures can be significant: non-zero numbers and zeroes that come after the demical place. 

\(\displaystyle 32.1\) has 3 significant figures while \(\displaystyle 0.003\) also has 3.

Therefore, your answer should also have 3 significant figures.

Example Question #761 : High School Physics

How many significant figures are in \(\displaystyle \small 20000kg\)?

Possible Answers:

Five

Four

Seven

One

Zero

Correct answer:

One

Explanation:

There are two categories that count as significant figures: non-zero numbers before the decimal point and everything after the decimal point. Since the number given is \(\displaystyle \small 20000kg\), there is only one non-zero number before the decimal point.

This number could have been rounded from any variation past the first digit, and we cannot assume that it is exact. To write this number in exact terms, we must use scientific notation or a decimal.

Example Question #2 : Understanding Significant Figures

How many significant figures should be in in the answer to the calculation?

\(\displaystyle -9.8\frac{m}{s^2}*100kg\)

Possible Answers:

One

Two

Three

Five

Four

Correct answer:

One

Explanation:

There are two categories that count as significant figures: non-zero numbers before the decimal point and everything after the decimal point.

When performing any operation between two numbers with different significant figures, always base it off the smallest number of significant figures. In this case, \(\displaystyle 100kg\) has only one significant figure; therefore our answer should also have only one significant figure.

Example Question #3 : Understanding Significant Figures

How many significant figures should be in the answer to the calculation?

\(\displaystyle 300\frac{m}{s}*2.00kg\)

Possible Answers:

Two

Six

One

Zero

Three

Correct answer:

One

Explanation:

Your answer should have the same number of significant figures as the term with the fewest significant figures. There are only two categories that qualify as significant figures: any terms after the decimal point and non-zero digits before the decimal.

In this problem, \(\displaystyle 300\frac{m}{s}\) has the fewest number of significant figures: only one. \(\displaystyle 2.00kg\) has three significant figures, but its precision is diminished by multiplying by a less precise term.

Example Question #3 : Understanding Significant Figures

Solve the expression with the proper number of significant figures.

\(\displaystyle 230.0 \div 200\)

Possible Answers:

\(\displaystyle 1.1\)

\(\displaystyle 1.2\)

\(\displaystyle 1\)

\(\displaystyle 1.0\)

\(\displaystyle 1.15\)

Correct answer:

\(\displaystyle 1\)

Explanation:

When multiplying or dividing, the answer must have the same number of significant figures as the term with the fewest significant figures in the problem. In this question, the one term (\(\displaystyle \small 200\)) has only significant figure, and the other term (\(\displaystyle \small 230.0\)) has four. Our final answer must match the term with the fewest significant figures: one. It is important to remember that zeroes after a decimal are significant figures, and determine the precision of a value. Zeroes before a decimal, such as in \(\displaystyle \small 200\), simply serve as place holders, and are no considered significant unless there is a decimal or scientific notation to clarify the term.

\(\displaystyle 230.0 \div 200=1.15\)

Round to the ones place to get an answer with only one significant figure.

\(\displaystyle 230.0 \div 200=1.15\approx 1\)

Example Question #4 : Understanding Significant Figures

Solve the expression with the proper number of significant figures.

\(\displaystyle 12.3 \times 4.2\)

Possible Answers:

\(\displaystyle 52\)

\(\displaystyle 51\)

\(\displaystyle 51.66\)

\(\displaystyle 52.0\)

\(\displaystyle 51.7\)

Correct answer:

\(\displaystyle 52\)

Explanation:

When multiplying or dividing, the answer must have the same number of significant figures as the term with the fewest significant figures in the problem. In this question, the one term (\(\displaystyle \small 4.2\)) has two significant figures, and the other term (\(\displaystyle \small 12.3\)) has three. Our final answer must match the term with the fewest significant figures: two.

\(\displaystyle 12.3\times 4.2 = 51.66\)

Round to the tens place to get an answer with only two significant figures.

\(\displaystyle 12.3\times4.2=51.66\approx 52\)

Example Question #5 : Understanding Significant Figures

How many significant figures should be in the solution to the given equation?

\(\displaystyle F=2.12kg*0.05\frac{m}{s^2}\)

Possible Answers:

One

Two

Six

Zero

Three

Correct answer:

One

Explanation:

Leading and trailing zeroes are not considered significant. To make this problem simpler, we may want to re-write the equation in scientific notation.

\(\displaystyle F=2.12kg*0.05\frac{m}{s^2}\)

\(\displaystyle F=(2.12kg)*(5*10^{-2}\frac{m}{s})\)

The first term still has three digits, all of which are significant. The second term, however, has been reduced to only one digit. Our term with the fewest significant figures determines how many significant figures should be in the solution. In this case, there would only be one significant figure in the solution.

Example Question #7 : Understanding Significant Figures

Which of the following numbers contains the greatest number of significant figures?

Possible Answers:

\(\displaystyle 7093000.084\)

\(\displaystyle 239.8401\)

\(\displaystyle 0.0000316\)

\(\displaystyle 6.279*10^{56}\)

\(\displaystyle 0092043.7600120\)

Correct answer:

\(\displaystyle 0092043.7600120\)

Explanation:

Significant figures are used to round scientific calculations in order to preserve precision. Every initial measurement will carry some degree of uncertainty or variation. It is important to carry that uncertainty to the final calculation, instead of unintentionally assigning greater certainty to the given values.

When determining significant figures, any zeroes that precede the first non-zero digit are considered insignificant and any zeroes that follow the final non-zero digit are considered insignificant. Any and all non-zero digits are significant. Sometimes it can help to write a number in scientific notation to identify significant figures.

\(\displaystyle 6.279*10^{56}\rightarrow4\ \text{significant figures}\)

\(\displaystyle 0.0000316=3.16*10^{-5}\rightarrow3\ \text{significant figures}\)

\(\displaystyle 239.8401=2.398401*10^2\rightarrow7\ \text{significant figures}\)

\(\displaystyle 7093000.084=7.093000084*10^6\rightarrow10\ \text{significant figures}\)

\(\displaystyle 0092043.7600120=9.2043760012*10^4\rightarrow11\ \text{significant figures}\)

Example Question #6 : Understanding Significant Figures

Which of the following answers does not have the correct number of significant figures associated with it?

Possible Answers:

\(\displaystyle 6.017*10^{-14}\rightarrow4\ \text{significant figures}\)

\(\displaystyle 0462.10\rightarrow4\ \text{significant figures}\)

\(\displaystyle 1260.007\rightarrow4\ \text{significant figures}\)

\(\displaystyle .098\rightarrow2\ \text{significant figures}\)

\(\displaystyle 0.098\rightarrow2\ \text{significant figures}\)

Correct answer:

\(\displaystyle 1260.007\rightarrow4\ \text{significant figures}\)

Explanation:

Significant figures are used to round scientific calculations in order to preserve precision. Every initial measurement will carry some degree of uncertainty or variation. It is important to carry that uncertainty to the final calculation, instead of unintentionally assigning greater certainty to the given values.

When determining significant figures, any zeroes that precede the first non-zero digit are considered insignificant and any zeroes that follow the final non-zero digit are considered insignificant. Any and all non-zero digits are significant. Sometimes it can help to write a number in scientific notation to identify significant figures.

\(\displaystyle 6.017*10^{-14}\rightarrow4\ \text{significant figures}\)

\(\displaystyle 0.098=9.8*10^{-2}\rightarrow2\ \text{significant figures}\)

\(\displaystyle .098=9.8*10^{-2}\rightarrow2\ \text{significant figures}\)

\(\displaystyle 0462.10=4.621*10^{2}\rightarrow4\ \text{significant figures}\)

\(\displaystyle 1260.007=1.260007*10^{3}\rightarrow7\ \text{significant figures}\)

Learning Tools by Varsity Tutors