Try this exercise!Shown below are two types of scales commonly used in the classroom --a spring scale (left) and a simple balance beam scale on the right.
On earth the spring scale reads 100g with an unknown mass attached at the bottom. To balance the scale on the right a 100g mass was also needed.
If we were to take both scales to the moon, what would the the spring scale read? How much mass would be needed to balance the 100g mass on the balance beam? Can you explain your answer? See if you are right by completing the questions below.
- What did the above experiment demonstrate? It shows that the scale on the left was measuring the force of gravity (weight) not mass. On earth the spring was standardized to read 100g at sea level. A true balance beam (like a triple beam balance you use at school) measures mass by balancing the scale against a known (standardized) mass. On the moon the mass on the left side of the balance may 'exert less force', but then less force will be needed to balance it.
- So what is really mass and weight if they are not the same thing?
- Mass is defined as the amount of matter an object has. One of the qualities of mass is that it has inertia As an example of inertia, imagine an ice puck resting on a frozen pond. It takes a certain amount of force to set the puck in motion. The greater the mass the more force will be needed to move the puck. The same is true if the puck were sliding along the ice. It would continue to slide until a force is applied to stop the puck. The more massive the puck is, the more force will be needed to stop the motion of the puck. Mass is a measure of how much inertia an object shows.
- The weight of an object on earth depends on the force of attraction (gravity) between the object object and earth. We can express that force as an equation:
- F = G[M m/r2] , where F is the force of attraction, M is the mass of the earth, m is the mass of the object, and r is the distance between the center of mass of the two objects (G is called the Gravitational Constant)
- What does this equation show? What will cause the force of attraction to increase or decrease? If either mass increases the force of attraction increases proportionally. Since the moon has 1/6 the mass of earth, it would exert a force on an object that is 1/6 that on earth.
- Why is the 1/r 2 factor so important? This is an inverse square relationship which seems to show up a lot in physics. How does it affect the force?
- What is 1/r 2 when r=1, 2, 5, 10? What is the decimal equivalent? Notice that when r=1 the value 1/r 2 is 1.0, but at r=10 it deceases to 1/100. That means gravity gets weak 'quick' as we move away from the earth.
- To get a real feel for the inverse square relationship, see if you can get two magnets. Move the poles closer and closer slowly, what do you notice when r (the distance between the poles) is very small?
FINDING THE MASS OF AN OBJECT
Mass is the amount of matter an object has. We often use a triple-balance beam to measure mass.
A triple-beam balance gets its name because it has three beams that allow you to move known masses along the beam.
Here is a picture of a triple beam balance. You probably have used one in school.
- There are also many other types of balances. Scientists need balances that can measure very small amounts of mass.
- If you are using a triple beam balance in school you might want to brush up on your skills on how to use a triple-beam balance
- Because a triple beam balance compares a known mass to an unknown mass it is unaffected by gravity. Unlike a spring scale which really measures weight, the triple beam balance gives a true measure of mass.
- Do you often get confused between mass and weight? Check out the Mass vs. Weight Page
VOLUME
- The volume of an object can be calculated geometrically using mathematical equations or by measuring liquid displacement.
- In the experiment below you will measure the volume of a cube using the formula V=(side)x(side)x(side) and by using a graduated cylinder to measure liquid displacement.
DENSITY OF A LIQUID
Problem: You are given two unknown liquids. Find the density of each. Materials: 100ml graduated cylinder, triple beam balance, calculator, 2 unknown liquids.
Procedure:
1) Find the mass of the empty graduated cylinder.
2) Pour unknown liquid #1 into the graduated cylinder to the 50 ml. level.
3) Find the mass of the graduated cylinder with 50ml of unknown liquid #1.
4) Repeat steps 1-3 for unknown liquid #2.
We can calculate density of a liquid using the formula:
Density= Mass/Volume
where mass is that for just the liquid (you must subtract out the mass of the graduated cylinder).
Now let's calculate the densities of the two liquids using the following given data.
Liquid #1:
Given: Mass of empty graduated cylinder = 78 grams
Mass of graduated cylinder with unknown liquid #1= 128 grams.
Find:
a) Mass of just the liquid = ____ b) Volume of liquid=_____ c) Density of liquid #1 =____
Liquid #2:
Given: Mass of empty graduated cylinder = 78 grams
Mass of graduated cylinder with unknown liquid #2= 117.5 grams.
Find:
a) Mass of just the liquid = ____ b) Volume of liquid =_____ c) Density of liquid #2=____
Check your answers by inserting the value in the box below.
What is each liquid?
Using the table below it is now possible for you to determine what each liquid is.
Densities for some common liquids are:
FINDING THE DENSITY OF A LIQUID USING A HYDROMETER
The density of a liquid can also be measured using a simple device known as a hydrometer.
Literally meaning "water measurer," a hydrometer is an instrument comprised of a vertical scale inside a sealed glass tube weighted at one end. It's used to measure the ratio (called specific gravity) of the density of a liquid grape to that of pure water.
A hydrometer is basically a sealed tube which is narrow at the top and is weighted with a dense material such as lead at the bottom. You may have seen one in a salt-water fish aquarium. The hydrometer is often considered the most valuable tool in wine making.
When a hydrometer is inserted into a liquid, the tube floats vertically so that the narrow part sticks out of the liquid while the heavy end sinks. The narrow part is calibrated for the density. The hydrometer floats higher in liquids of higher density and lower in liquids of lower density.
DENSITY
ake a look at the two boxes below. Each box has the same volume. If each ball has the same mass, which box would weigh more? Why?
The box that has more balls has more mass per unit of volume. This property of matter is called density. The density of a material helps to distinguish it from other materials. Since mass is usually expressed in grams and volume in cubic centimeters, density is expressed in grams/cubic centimeter.
We can calculate density using the formula:
Density= Mass/Volume
In the previous lesson you calculated the mass and volume of two blocks. If you would like to review these sections click on the appropriate links shown at the left.
Block I
Mass = 79.4 grams
Volume=29.8 cubic cm.
Block II:
Mass= 25.4 grams
Volume=29.8 cubic cm.
Now Let's calculate the density for each of these blocks.
