Measurements and units are important in science because they provide a common language that allows us to communicate information.
There are two main systems of measurement
The Metric System - This system is used in most of the world and it utilizes a base 10 system with corresponding prefixes. Typically, the scientific community adheres to this system, measurements include base units such as meters, grams, and liters.
The Standard American Engineering System - This is primarily used in the United States and contains units such as inches, pounds, and gallons.
Length Measurement Typically a metric ruler is used to determine the length of an object. To measure length, use either centimeter (cm) or millimeters (mm). You should know how to covert millimeters to centimeters and vice versa. The metric ruler we are working with is calibrated – or scaled – in centimeters.
Volume Measurement A graduated cylinder is often used to measure a liquid’s volume, or the space it occupies. Liters and milliliters are typically used to indicate volume in the metric system. Graduated cylinders are calibrated in milliliters (mL). Water and many other fluids form a meniscus (curving surface) when placed in the narrow tube of a graduated cylinder. To correctly read the volume of the liquid, place the cylinder on a flat surface. Then read from the bottom of the curved meniscus at eye level.
Mass Measurement Mass – the quantity of matter in something – is often measured with a balance, which is a tool that compares an object of unknown mass with an object of known mass. The triple-beam balance or an electronic balance are typically used in this capacity. The mass of the object is the sum of the readings on the three beams.
Scalar and Vector Quantities
All quantities in physics are classified as scalar or vector. A scalar quantity is described by a numerical value that represents a fixed measurement (i.e., distance and speed). A vector quantity is described by a numerical value as well as a direction (i.e., velocity).
Nothing in the universe stays still; from the organs in your body digesting and processing food, to the Earth orbiting the sun. The universe is in a constant state of motion. We measure motion through speed and velocity. Speed is a scalar quantity that measures distance over time. Velocity is similar, however it measures displacement over time and is a vector quantity.
Example: (Image and Question taken from physics classroom) Use the diagram to determine the average speed and the average velocity of the skier during the three minutes.
Formula: speed = distance/time Speed = 140 m/min (420 m /3 min) The skier traveled a total distance of 420 m in 3 minutes A --- B = 40 m + 100 m + 40 m = 180 m B --- C = 40 m + 100 m = 140 m C --- D = 100 m Total Distance: 180 m + 140 + 100 m = 420 m
Formula: velocity = displacement/time Speed = 46.7 m/min, right (140 m) /3 min) The skier's overall position change 140 m in 3 minutes, from start to finish. A --- D = 40 m + 100 m = 140 m Total Displacement: 140 m Since the skier's position moved towards the right we must include that in our answer.
Remember: Since velocity is a vector quantity it must always have a direction.
Many students have difficulty converting between units because, even with the conversion factor, they are unsure whether they should divide or multiply. This becomes even more confusing if there are multiple units needed to be converted
Example: Convert 565,900 seconds into days 565,900 sec1 min1 hr1 day = 6.55 days 1 60 sec 60 min 24 hr
Comparing Distance and Displacement
Distance and displacement are interrelated measures that describe the relationship between two points. Distance is a scalar quantity that measures all positional changes of an object. Displacement is a vector quantity that is the overall change in position of an object.
Example: If a physics teacher walks 5 meters West, 1 meter South, 5 meters East, and 1 meter North. What is the total distance traveled and what is the displacement of the teacher?
Distance = 12 m (5m + 1m + 5m + 1m) Displacement = 0 m (Since the teacher traveled the same distance North and South as well as East and West the overall change in position will be the same. In other words he ends up in the same position that he starts)
Speed, velocity and acceleration all describe motion but they are not the same. Speed and velocity are the rate at which an object's position changes. Acceleration is a vector quantity that describes the change in velocity. If an object changes speed or direction it's accelerating.
Example: A truck going 60 mph accelerates to pass a car, westward. Ten seconds later the truck is going 80 mph. Calculate the acceleration of the car.
Formula: acceleration = change in velocity/ change in time Acceleration = 80 mph - 60 mph / 10 s - 0 s = 20 mph / 10 s = 2 mph / s, westward The car initially starts at 60 mph but accelerates to 80 mph, the change in velocity is 20 mph over a 10 s interval of time.
Remember: Since acceleration is a vector quantity it must always have a direction, when provided.