# Relating length volume and mass relationship

### Fundamentals of Physics/Physics and Measurement - Wikibooks, open books for an open world

2 Length, Mass and Time; 3 Dimensional and Unit Analysis; 4 Density While it was previously defined as a specific volume of water (e.g. 1 liter or a 10 cm³ cube ), its current different densities, and density may be relevant to buoyancy, purity and packaging. A conversion factor is a ratio between two compatible units. Density is the mass per unit of volume of a substance. The density equation is: Density = MassVolume. To solve the equation for Mass. Definition of matter and what mass and volume measure. The two are closely related, but they measure different things. For example, the volume of a rectangular solid is the product of its length, width, and height. For example, the volume of a rectangular room can be calculated with the formula.

When doing calculations, you should only keep at most 1 doubtful digit; while it is acceptable to keep them when using a handheld calculator or computer, the final answer should be adjusted to reflect the correct number of significant digits.

The current metric system also includes the following units: An ampere A is a measure for electric current. A kelvin K is a measure for temperature. A mole mol is the amount of substance based on number of atoms rather than mass.

A candela cd is a measure for luminous intensity. The Lumen lm is a measure unit for total amount light visible for the human eye emitted by a source. We suggest that students begin by matching pennies on the left with pennies on the right and they should discover that all pennies aren't really the same--this is real! After the students become familiar with the use of the balance, we suggest that nearly equal volumes of the assorted materials sand, rice, metal shot, Styrofoam be measured.

If you are using the 1 oz Dixie portion cups, it is possible to draw a line on the cup 1. A very important question to consider now is: If you used this Mass Balance on the moon or on Mars, would the same amount of material on one side require the same number of pennies on the other side to balance it as it did on Earth?

Naturally there is no easy way for us to perform such an experiment but, having your students think about this should help them to start understanding the difference between weight and mass.

Mass or as Newton would say, the quantity of matter in an object, does not change when you change your location in space but, as we will see shortly, weight does change.

Using a carefully segmented straw, a bent paper clip, a rubber band, some string, a small cup, a 3X5 card and some scotch tape we will construct the "Weight Scale" shown below: Since we had difficulty in joining the segment of rubber band to the string, we decided to show you a "carrick bend" which works quite well for this situation. A simple slip knot works well on the bottom where the rubber band attaches to the bent paper clip bail.

A later construction detail diagram will give you a better illustration of the Weight Scale. The students will calibrate this Weight Scale with pennies and mark the 3 X 5 card with a marking pen during the calibration exercise. Attaching the rubber band to the bail of the cup is easily accomplished with a slip knot but attaching the string to the rubber band is a slight problem--a suggested knot is shown with the illustration.

The whole idea is to have the zero of the scale at the bottom of the card using the string-rubber band junction as the pointer. With about 25 pennies in the cup, the rubber band will stretch to about the top of the card.

You hold the scale with the string which has been passed through a small piece of straw taped to the card. The students will carefully load the cup with pennies and mark the card at about 5 penny intervals.

A more detailed construction of the Weight Scale is shown "below. Note that in the construction diagram "below", we show how the straw should be sectioned so that it can be attached to the 3 X 5 card. In the final scale, naturally, the string and rubber band fit inside of the straw sections.

It is important that the lower length of the straw be made just long enough to extend from the top of the paper clip "bail" to the bottom of the card with the rubber band sticking out the top.

## Fundamentals of Physics/Physics and Measurement

You must be able to tie the rubber band to the string and have the junction of the two be on the lower end of the 3 X 5 with nothing in the cup. This is the "below" referred to in the above paragraph.

We decided it would take a large image to show the necessary details so, if you have the time, click here for Weight Scale Construction Details. After the students have calibrated the Weight Scale, it might be fun to have them see if they can guess how many pennies have been loaded into their cup by another student.

From this they will learn how to read between the marks they have placed on their cards this is called interpolation and they will also learn that the scale is really not too accurate. However, all instruments are less than perfect at some level and this crude scale should help them to realize this fact. We think it is nice that the scale is quite inexpensive and students who wish can construct one at home. This Weight Scale can also be used to measure some of the other materials that were measured with the Mass Balance.

Hopefully they will find that they will get pretty close to the same answer in "pennies" for the mass as measured on the Mass Balance and the weight as measured on the Weight Scale. So you ask--what is the difference between weight and mass? Now comes the key question to ask the class: If you took the Mass Balance and your calibrated Weight Scale to the Moon, do you think they would give the same measurement as on Earth? Remember, you always balance the unknown object against several pennies with the Mass Balance but you just let the unknown object pull down against the calibrated rubber band on the Weight Scale.

- How do you calculate mass using density and volume?

We hope that this thought experiment will help the students see that the Mass Balance will measure the same no matter where you locate it in space but the Weight Scale, which measures how hard gravity pulls down on the object, will give a smaller reading on the moon. This is confusing stuff and most college students will have difficulty understanding it. Perhaps if your kids start thinking about it early enough, they may come to a better understanding of the difference between weight and mass when they are older.

Since density is mass per volume, the most straight forward way of measuring the density of something is to measure its mass, then measure its volume and divide the mass by the volume. We could do exactly that in this activity but at this point we have no good way to measure volume. If you have a graduated cylinder they aren't expensive but most elementary schools don't have them you could use it with some water to mark the small "portion cups" at specific volumes.

We have already suggested that the small 1 oz cups will hold 10 cubic centimeters when filled to a point 1. Rather than actually measuring the density, we feel it will be sufficient for the students to appreciate that the same volume can be a large mass or a small mass depending upon the material involved. Our plan is to have the same volume of several different materials and measure their mass with the Mass Balance.

Hopefully this exercise will help the students to begin to see the relationship between mass, volume and density. The next page begins the "Student Activity Sheet". We suggest that these be reproduced in sufficient numbers for the entire class.

Whether the students work individually or in groups is best decided by you, however, some of the exercises need at least two people to hold and use the apparatus. Mass, Weight and Density--how matter is measured, how it interacts with other matter and how it fills space.

Which is heavier, a pound of feathers or a pound of lead?

### BBC Bitesize - GCSE Physics (Single Science) - Density - Revision 1

If you have never heard this old trick question before--think about it. Now try this one: Finally, think about this one: The answer to each of these questions requires that you understand the difference between mass, weight and density.

You will measure the mass of objects by comparing them to the mass of pennies with a thing we will call a "Mass Balance". Although mass is usually measured in kilograms or grams, we will measure mass in "pennies". The Mass Balance is shown below. This balance measures mass in "penny" units. First test the Mass Balance to see if it is "zeroed". When you lift it by the center paper clip, it should stay fairly level.

When the clip is in the top hole, it will balance easily. If you put the clip in the bottom hole, it probably will be too sensitive to balance at all.

Test the Mass Balance by placing 5 pennies in both cups and gently lift it off the table--it should balance. Have one student secretly place a number of pennies in one cup and see if you can figure out how many pennies there are in the cup by matching them with pennies in the other cup.

Although mass and volume are properties you deal with every day, the idea of density is a little less obvious and takes careful thought. However, once you get the hang of it, density is very useful.

To get density, divide mass by volume. For example, a lead brick, 5 cm x 2 cm x 10 cm, weighs 1, g. Divide 1, by to get the density of lead, Mass is not completely understood, so it is defined in two very different ways: Inertial mass measures how strongly an object resists acceleration, while gravitational mass measures how strongly an object attracts other things to itself.

Strictly speaking, a scale measures weight, but you can usually think of weight and mass as the same thing.

**How to Take Measurements of Length, Volume and Mass**