# Article: Basic Techniques of Physics Measurement

In the realm of physics, measurements are fundamental. They provide the numbers to the theories and formulas that help us understand the natural world in a quantitative way. This article will focus on the basic techniques of physics measurement.

## Measuring Lengths

Length measurements are often taken with rulers, tape measures, or calipers. The choice of a tool depends on the precision required. For instance, the smallest scale of a common ruler is usually 1mm, an engineer’s caliper can measure up to .01mm, and even more precise measurements can be made with a micrometer.

## Measuring Mass

The mass of an object is typically measured with a balance. The basic principle is comparing the unknown mass to a known mass. For precision, a triple beam balance can be employed. However, for everyday science projects and teaching purposes, a simple electronic balance can do the job just fine.

## Measuring Time

Time is commonly measured using clocks and watches. In experiments requiring high precision, atomic clocks are employed. For measuring shorter periods, chronometers, stopwatches, or electronic counters can be utilized.

## Measuring Temperature

Temperature is the measure of the average kinetic energy of a substance’s particles. The most common tool for measuring temperature is a thermometer. There are digital and mercury thermometer types. For extreme temperatures, pyrometers are often used.

## Units and Dimensions

In physics, we use the International System of Units (SI) for measurements. The basic units include the meter for length, kilogram for mass, second for time, and Kelvin for temperature.

## Uncertainty and Errors

All measurements have a degree of uncertainty due to various factors like instrument precision, observational error, etc. An essential part of any measurement is estimating the error or uncertainty in the measurements.

The following problems will provide a practical glimpse into the concepts explained above.

## Problems

1. A piece of wood is measured to be 150.0 mm long using a ruler marked in millimeters. What is the length of the wood in meters?

Solution:

To convert from millimeters (mm) to meters (m), divide the value by 1000 since there are 1000 mm in a meter.

Length in m $=\frac{150.0}{1000}=0.150 m$

2. A student measures the mass of an apple to be 0.152 kg. What is the mass of the apple in grams?

Solution:

To convert from kilograms (kg) to grams (g), multiply the given value by 1000 since there are 1000 g in a kg.

Mass in g $=0.152 * 1000=152 g$

3. A stopwatch records a time of 52.33 seconds. How many minutes is this?

Solution:

To convert from seconds to minutes, divide the value by 60 as there are 60 seconds in a minute.

Time in minutes $=\frac{52.33}{60}=0.872 minutes$

4. The temperature outside is measured to be 35.0 degrees Celsius. What is the temperature in Kelvin?

Solution:

To convert from Celsius to Kelvin, add 273.15 to the given value as the freezing point of water is 0 degrees Celsius or 273.15 Kelvin.

Temperature in K $=35.0 + 273.15=308.15 K$

5. A child is running a 100-meter dash and finishes in 12.50 seconds. What is the child’s average speed?

Solution:

Speed is the distance travelled per unit time. Therefore, to find the speed, divide the distance by the time.

Speed $=\frac{distance}{time}=\frac{100}{12.50}=8 m/s$

6. An object’s mass is measured to be 7.2 kg with an instrument that has an uncertainty of 0.2%. What is the uncertainty in the object’s mass?

Solution:

The uncertainty in a measurement is often given as a percentage of the measured value. Therefore, to find the uncertainty, multiply the percentage uncertainty by the measured value.

Uncertainty $=\frac{percentage uncertainty}{100} * measured value=\frac{0.2}{100} * 7.2=0.0144 kg$

7. The length of an object is measured three times and the values obtained are 11.2 cm, 11.3 cm, and 11.1 cm. What is the average length?

Solution:

The average length is the sum of all the values divided by the number of values.

Average length $=\frac{sum of values}{number of values}=\frac{11.2+11.3+11.1}{3}=11.2 cm$

8. A box is 50.0 cm long, 20.0 cm wide, and 10.0 cm high. What is the volume of the box?

Solution:

The volume of a rectangular box (or prism) is its length times its width times its height.

Volume $=length * width * height=50.0*20.0*10.0=10,000 cm^3$

9. A student finds that the period of a pendulum, the time for one swing, is 2.40 seconds. If the student measures the period ten times and finds an average period of 2.37 seconds, what is the percentage error in the period?

Solution:

The percentage error is given by the absolute value of the difference between the measured and accepted value divided by the accepted value, all multiplied by 100.

Percentage error $=\frac{|measured – accepted|}{accepted}*100=\frac{|2.37 – 2.40|}{2.40}*100=1.25%$

10. During a physics lab, a student measures the height of a table three times and obtains values of 1.202 m, 1.200 m, and 1.198 m. What is the student’s measurement with the correct number of significant figures?

Solution:

When taking the average of several measurements, the number of significant figures in the average is equal to the number in the least precise measurement. Therefore, the average of the three measurements is 1.200 m, with four significant figures.

The rest of the problems and solutions can be found in this source. Please note that the LaTeX used in these solutions are simple arithmetic calculations. For more complex equations, additional LaTeX syntax would be required.

These exercises showcase the practical application of basic measurement techniques in physics. It is important to understand that all measurements have inherent uncertainties, and thus, the need for careful and multiple measurements, error estimation, and data representation is absolutely essential.

Remember, as with everything else in physics (and life), practice makes perfect. So keep working on those measurements and their related calculations to achieve perfection.