Sphero's weight, mass, and density
The Science
Sphero is a physical object. It has mass and it has weight. We will use mass to determine buoyancy. Yes, Sphero floats.
Mass is the amount of matter an object has. The mass of an object remains the same or constant.
The weight of an object is the affect of gravity on an object. The weight depends on the gravity. The gravity on Earth is constant for our purposes. Gravity is affected by altitude on Earth. There is a close connection between mass and weight but they are two separate things.
Gravity relies on the mass of the Earth. It also relies on the elevation of the object weighed. Objects on the surface of the earth feel a greater pull by gravity. Objects in orbit around the earth, like a satellite, don’t feel the pull of gravity as much. This is why objects in space are said to be weightless.
An astronaut on earth could weigh about 200 pounds. In space that same astronaut’s weight can’t be measured. This is because there is not gravity to push down on the weight scale.
This is what makes mass different from weight. The astronaut has not changed. His or her matter has remained the same. Everything is made of matter. Some matter is light and some is heavy. The measurement of this amount of matter is called mass. The more matter something has the greater it’s mass.
Sphero’s Weight
There are a variety of ways to weigh Sphero. The easiest is to use a kitchen scale. Sphero comes with a base for charging. We will use this base to prevent it from rolling off the scale. Get yourself a kitchen scale. Turn on the kitchen scale and place the charging base on the scale. The scale will read the weight of the charging base.
We need to subtract this weight. There are a couple of ways to do this. The most obvious way is to take the base weight and subtract it from the total weight after adding the Sphero. Another way to eliminate the base weight is to use the Tare option on the scale. Most modern kitchen scales have this option. There is usually a button on the scale that reads Tare.
To use the Tare, press the Tare button on the scale. The scale will eliminate the base’s weight and display a zero. Just like the base was not on the scale.
Place Sphero on the base and read the weight on the scale. In Standard measurement, Sphero weighs approximately 6.35 ounces. In the Metric System, Sphero weighs 180 grams.
Sphero’s mass is 180 grams. The scale compensates for Earth’s gravity. Earth has a constant gravitational pull of 9.807 meters per second squared. The scale eliminates this force from our value.
A Balance scale
Let’s use a balance scale to check our value. Balance scales are used to measure mass. We use a balance scale to measure the mass of one object with the mass of another. We place one object on one side of the scale. On the other side we place objects that have a known mass. The objects are usually metal weights.
The mass of the weights is marked on each. We place enough of these weights until the scale is balanced. The total mass placed on the scale is used as a measure of the mass on the other side.
The the value of the weights placed on the other side of the balance total 180 grams. This agrees with the value from the kitchen scale.
This is part of the scientific process. We take measurements and then we need to verify those measurements. If the measurements are different then we need to understand why.
Buoyancy and Density
We know that Sphero floats. It is water tight. Make sure there are not cracks on your Sphero. These lessons cover buoyancy, density, and water displacement.The buoyancy of something depends on its density. Water has a density of 1. Objects that have a density greater than one will sink. Objects that have a density less than one will float. We will calculate the density of Sphero in a moment.
First, we need to know how we arrived at the density of water. Place a beaker on the kitchen scale. Press the Tare button to set the scale to zero. Pour 250 mL of water into the beaker. Read the measurement on the scale. Make sure the measurement units are in grams. The measurement is the same as the amount of milliliters we placed in the beaker.
To determine the density of water we divide the mass by the volume. The volume in milliliters is 250. The mass in grams is 250. The answer is one. The density of water is one.
Sphero’s Density
Sphero is enclosed in a plastic sphere. We will place Sphero into water and use it to learn about buoyancy and density. Buoyancy is the capacity for something to float. The density of an object has much to do with its ability to float.
We need a container with water. The container needs to have a way for us to measure the amount of water. A beaker is a good container to use if you have one large enough. I find that a two-cup kitchen measuring cup works well if a beaker isn't available. These measuring cups are available at any discount store for a few dollars. They have a nice handle to hold onto.
Fill the container to the one-cup measurement. Add some food coloring to help you see the water level if necessary.
Insert Sphero into the measuring cup. Sphero displaces the water in the measuring cup. Sphero forces the water up and around the measuring cup. The water level rises to one-and-three-quarter cups. Sphero displaces three-quarters of a cup of water.
Sphero doesn't completely float and it doesn't completely sink either. This is due to Sphero’s density.
To find the density of an object we need to divide the mass of the object by the volume. This is where all the math we did earlier comes together.
Sphero has a mass of 180 grams. It has a volume of 180 cubic centimeters. Sphero’s density is One! This is the same density as that of water. This explains why most of Sphero is submerged in water. Much like an iceberg.
All the science we just did would not be possible without the math we used in the previous lessons. This is that math science connection we are always wanting to make with students.
