Objectives
- Reinforce your ability to use unit conversions in real-world and scientific contexts.
Section 5.2 Explore
Worksheet 5.2.1 Explore: Unit Conversions
This worksheet is designed to help you explore the concept of unit conversions in physics.
1.
The Mars rover Perseverance launched from Cape Canaveral, Florida, on July 30, 2020, aboard an Atlas V 541 rocket. Its main engine, the RD-180, burned a mix of liquid oxygen and rocket-grade kerosene to produce the thrust needed for takeoff. The total mass of fuel used by the main engine during launch was about 284 megagrams. Write this mass in scientific notation using SI units.
Hint.
Mega means \(10^6\text{.}\) So, 284 megagrams can be written as \(284 \times 10^6\) grams. However, the SI unit of mass is not grams, it’s kilograms.
Answer.
\(2.84 \times 10^{5}\) kg.
Solution.
284 megagrams can be written as \(284 \times 10^6\) grams.
The SI unit of mass is kilograms, not grams. To convert grams to kilograms, divide by \(10^3\) (or multiply by \(10^{-3}\)). So, \(284 \times 10^6\) grams is equal to \(\frac{284 \times 10^6}{10^{3}}\) kg.
Simplifying this gives us \(284 \times 10^{3}\) kg.
Finally, we can express this in scientific notation as \(2.84 \times 10^{5}\) kg.
Therefore, the mass of fuel used by the main engine during launch is \(2.84 \times 10^{5}\) kg.
2.
During its decent onto the surface of Mars, the Perseverance moved through the Martian atmosphere which can contain dust particles roughly 2.5 micrometers in diameter. Write the diameter of the dust particles in scientific notation using SI units.
Hint.
Micro means \(10^{-6}\text{.}\) And the SI unit of length is meters.
Answer.
\(2.5 \times 10^{-6}\) m
Solution.
2.5 micrometers can be written as \(2.5 \times 10^{-6}\) meters.
Meters is the SI unit of length, so we don’t need to convert it.
Therefore, the diameter of the dust particles is \(2.5 \times 10^{-6}\) m.
3.
The data collected by the Perseverance rover is transmitted back to Earth. It can take about 300 seconds for the data to reach Earth from Mars. Use unit conversions to express the time it takes for data to reach Earth. Keep the same unit of seconds, just add a prefix.
Hint.
There are many options, but it’s common to have the value between 1 and 10 when the original value has one sig fig. So your answer could be 3 "prefix"seconds.
Answer.
3 hectoseconds.
Solution.
Rewrite 300 seconds as \(3 \times 10^2\) seconds.
The prefix "hecto" means \(10^2\text{.}\)
Therefore, 300 seconds can be expressed as 3 hectoseconds.
For fun: you can also say 30 decaseconds, 30,000 centiseconds, etc...
4.
The data collected by the Perseverance rover can be directly transmitted back to Earth from the rover. The rate at which this data is transferred is about 32,000 bits per second. Use unit conversions to express the rate data is transferred from the rover to Earth. Keep the same unit of bits per second, just add a prefix.
Hint.
There are many options, but it’s common to have the value between 10 and 100 when the original value has two sig figs. So your answer could be 32 "prefix"bits per second.
Answer.
32 kilobits/second
Solution.
Rewrite 32,000 bits/second as \(32 \times 10^{3}\) bits/seconds.
The prefix "kilo" means \(10^3\text{.}\)
Therefore, 32,000 bits per seconds can be expressed as 32 kilobits per second.
For fun: you can also say .032 megabits per second, 3,200,000 centibits per second, etc...
