Weight, Mass, and Volume Relationships of soil » Geotechnical Engineering | Civil Engineering
We hope we can explain the difference between mass, weight and density so .. students to begin to see the relationship between mass, volume and density. The mass of an object is a fundamental property of the object; a numerical The weight of an object is the force of gravity on the object and may be defined as the mass times the acceleration of gravity, w = mg. Density is mass/volume. Density is defined as mass per unit volume; mathematically, we would write: or mass m density d relationship between mass and volume of the substance.
Buoyancy and weight[ edit ] Regardless of the fluid in which an object is immersed gas or liquidthe buoyant force on an object is equal to the weight of the fluid it displaces. A hot air balloon when it has neutral buoyancy has no weight for the men to support but still retains great inertia due to its mass. Usually, the relationship between mass and weight on Earth is highly proportional; objects that are a hundred times more massive than a one-liter bottle of soda almost always weigh a hundred times more—approximately 1, newtons, which is the weight one would expect on Earth from an object with a mass slightly greater than kilograms.
A common helium-filled toy balloon is something familiar to many. When such a balloon is fully filled with helium, it has buoyancy —a force that opposes gravity. When a toy balloon becomes partially deflated, it will often become neutrally buoyant and can float about the house a meter or two off the floor. In such a state, there are moments when the balloon is neither rising nor falling and—in the sense that a scale placed under it will have no force applied to it—is, in a sense perfectly weightless actually as noted below, weight has merely been redistributed along the Earth's surface so it cannot be measured.
Though the rubber comprising the balloon has a mass of only a few grams, which might be almost unnoticeable, the rubber still retains all its mass when inflated. If one were however to weigh a small wading pool that someone then entered and began floating in, they would find that the full weight of the person was being borne by the pool and, ultimately, the scale underneath the pool.
However, as noted, an object supported by a fluid is fundamentally no different from an object supported by a sling or cable—the weight has merely been transferred to another location, not made to disappear. The mass of "weightless" neutrally buoyant balloons can be better appreciated with much larger hot air balloons.
Buoyancy and the resultant reduction in the downward force of objects being weighed underlies Archimedes' principlewhich states that the buoyancy force is equal to the weight of the fluid that the object displaces. If this fluid is air, the force may be small.
Buoyancy effects of air on measurement[ edit ] Normally, the effect of air buoyancy on objects of normal density is too small to be of any consequence in day-to-day activities. For convenience, a standard value of buoyancy relative to stainless steel was developed for metrology work and this results in the term "conventional mass".
Since objects with precisely the same mass but with different densities displace different volumes and therefore have different buoyancies and weights, any object measured on this scale compared to a stainless steel mass standard has its conventional mass measured; that is, its true mass minus an unknown degree of buoyancy.
In high-accuracy work, the volume of the article can be measured to mathematically null the effect of buoyancy.
Soil Phase Relationships
Types of scales and what they measure[ edit ] A balance-type weighing scale: Unaffected by the strength of gravity. Load-cell based bathroom scale: Affected by the strength of gravity. This is because balances "dual-pan" mass comparators compare the gravitational force exerted on the person on the platform with that on the sliding counterweights on the beams; gravity is the force-generating mechanism that allows the needle to diverge from the "balanced" null point.
These balances could be moved from Earth's equator to the poles and give exactly the same measurement, i. But if you step onto spring-based or digital load cell -based scales single-pan devicesyou are having your weight gravitational force measured; and variations in the strength of the gravitational field affect the reading. In practice, when such scales are used in commerce or hospitals, they are often adjusted on-site and certified on that basis, so that the mass they measure, expressed in pounds or kilograms, is at the desired level of accuracy.
NIST Handbook states: The weight of an object is a measure of the force exerted on the object by gravity, or the force needed to support it. The pull of gravity on the earth gives an object a downward acceleration of about 9. In trade and commerce and everyday use, the term "weight" is often used as a synonym for "mass. The use of the term "mass" is predominant throughout the world, and is becoming increasingly common in the United States. Use of the Terms "Mass" and "Weight.
The term "weight" appears when inch-pound units are cited, or when both inch-pound and SI units are included in a requirement. The terms "mass" or "masses" are used when only SI units are cited in a requirement. The following note appears where the term "weight" is first used in a law or regulation. The metric system was designed so that water will have a density of one gram per cubic centimeter or kilograms per cubic meter.
Lead is about 10 times as dense as water and Styrofoam is about one tenth as dense as water. II Purpose of the Activity: The purpose of this activity is to investigate the meaning of mass, weight and density by looking at how each might be measured. III Materials required for the Activity: Lead shot can be obtained at a gun and ammo shopany other finely ground solid material which can be used to illustrate a variety of different densities. We have avoided liquids since they seem to make a bigger mess.
IV What the teacher must do in advance of the activity: We feel the most difficult preparation item for this activity will be making the drilled ruler or preparing sections of wood properly drilled. Is it possible to assign tasks like this to parents who have better shop facilities at home? These will become the balance beams for our mass balance.
The actual dimensions of the balance beam is not too critical and a wooden ruler is about right--the best are old ones that have lost the metal strip they often have along one edge. What follows is a description and illustration of how the balance beam should be constructed: The center hole should be exactly in the center so that when the beam is supported by a nail through this center hole, it will spin around freely. The two end holes should be in line with the center hole and equidistant on each side.
Two other holes should be drilled on a line directly above the center hole. We sincerely hope it will not be too difficult for you to accomplish this. We fooled around with metal hangers, etc.
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It will be necessary to poke holes in the portion cups. Should you do this in advance or can your students do it? A small nail works well for this purpose. Probably time could be saved in class if the necessary strings were cut to length in advance and perhaps even tied to the cups. Building the "Weight Scale" requires some careful cutting of a straw that can be done with a good pair of scissors or a sharp knife.
We think kids can do all of it but it will take time. You should build one prototype Weight Scale in advance so you can work out the details of construction and decide how much of the cutting should be done in advance.
Teaching outline and Presentation suggestions: Once again we remind you that we really don't know the best way to teach these concepts to young students. The following are suggestions for construction and use of the equipment and how we envisioned one might use this stuff but only you can know the best way to present this material to your students.
Mass is usually measured with a balance. The idea is to compare the unknown object with the mass of a known amount. Illustrated below is the device we will use to measure mass and we will call it "the Mass Balance".
Since everyone seems to have lots of pennies and all pennies are about the same mass, we will use the penny as our standard of mass. It turns out that the average penny has a mass of about 2. The mass measurement is accomplished simply by placing the unknown object in one cup of the Mass Balance and finding out how many pennies placed on the other side it takes to achieve balance. You should first check the Mass Balance with nothing in either cup to see if it is properly "zeroed".
You should notice that the balance is most sensitive when the upper paper clip is in the center hole in fact it is really too sensitive here and it will be less sensitive when you use the higher holes. Slight errors in the zero reading can be corrected by using shorter or longer string sections on the appropriate side.
Make sure all paper clips rotate freely in the drilled holes.
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The balance will not work properly if the paper clips hang up. The Mass Balance can be loaded with the cups on the table and pulling upward slightly on the support paper clip will test the balance condition. 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. 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. 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.
Mass versus weight
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? 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".