Physics and Mass Help (page 2)
The earliest physicists were curious about the way matter behaves: What happens to pieces of it when they move or are acted on by forces. Scientists set about doing experiments and then tried to develop mathematical models (theories) to explain what happened and that would predict what would occur in future situations. Classical mechanics is the study of mass, force, and motion.
The term mass , as used by physicists, refers to quantity of matter in terms of its ability to resist motion when acted on by a force . A good synonym for mass is heft . Every material object has a specific, definable mass. The Sun has a certain mass; Earth has a much smaller mass. A lead shot has a far smaller mass still. Even subatomic particles, such as protons and neutrons, have mass. Visible-light particles, known as photons , act in some ways as if they have mass. A ray of light puts pressure on any surface it strikes. The pressure is tiny, but it exists and sometimes can be measured.
Mass Is A Scalar
The mass of an object or particle has magnitude (size or extent) but not direction. It can be represented as a certain number of kilograms, such as the mass of the Sun or the mass of the Earth. Mass is customarily denoted by the lowercase italicized letter m .
You might think that mass can have direction. When you stand somewhere, your body presses downward on the floor, the pavement, or the ground. If someone is more massive than you, his or her body presses downward too, but harder. If you get in a car and accelerate, your body presses backward in the seat as well as downward toward the center of the Earth. But this is force, not mass. The force you feel is caused in part by your mass and in part by gravity or acceleration. Mass itself has no direction. If you go into outer space and become weightless, you will have the same mass as you do on Earth (assuming that you do not lose or gain mass in between times). There won’t be any force in any direction unless the space vessel begins to accelerate.
How Mass Is Determined
The simplest way to determine the mass of an object is to measure it with a scale. However, this isn’t the best way. When you put something on a scale, you are measuring that object’s weight in the gravitational field of the Earth. The intensity of this field is, for most practical purposes, the same wherever you go on the planet. If you want to get picayune about it, though, there is a slight variation of weight for a given mass with changes in the geographic location. A scale with sufficient accuracy will show a specific object, such as a lead shot, as being a tiny bit heavier at the equator than at the north pole. The weight changes, but the mass does not.
Suppose that you are on an interplanetary journey, coasting along on your way to Mars or in orbit around Earth, and everything in your space vessel is weightless. How can you measure the mass of a lead shot under these conditions? It floats around in the cabin along with your body, the pencils you write with, and everything else that is not tied down. You are aware that the lead shot is more massive than, say, a pea, but how can you measure it to be certain?
One way to measure mass, independently of gravity, involves using a pair of springs set in a frame with the object placed in the middle (Fig. 7-1). If you put something between the springs and pull it to one side, the object oscillates. You try this with a pea, and the springs oscillate rapidly. You try it again with a lead shot, and the springs oscillate slowly. This “mass meter” is anchored to a desk in the space ship’s cabin, which is in turn anchored to the “floor” (however you might define this in a weightless environment). Anchoring the scale keeps the whole apparatus from wagging back and forth in midair after you start the object oscillating.
A scale of this type must be calibrated in advance before it can render meaningful figures for masses of objects. The calibration will result in a graph that shows oscillation period or frequency as a function of the mass. Once this calibration is done in a weightless environment and the graph has been drawn, you can use it to measure the mass of anything within reason. The readings will be thrown off if you try to use the “mass meter” on Earth, the Moon, or Mars because there is an outside force, gravity, acting on the mass. The same problem will occur if you try to use the scale when the space ship is accelerating rather than merely coasting or orbiting through space.
Mass Practice Problems
Suppose that you place an object in a “mass meter” similar to the one shown in Fig. 7-1 . Also suppose that the mass-versus-frequency calibration curve for this device has been determined and looks like the graph of Fig. 7-2 . The object oscillates with a frequency of 5 complete cycles per second (that is, 5 hertz or 5 Hz). What is the approximate mass of this object?
Fig. 7.1 . Mass can be measured by setting an object to oscillate between a pair of springs in a weightless environment.
Fig. 7.2 . Graph of mass versus oscillation frequency for a hypothetical “mass meter” such as the one shown in Fig. 7-1 .
Locate the frequency on the horizontal scale. Draw a vertical line (or place a ruler) parallel to the vertical (mass) axis. Note where this straight line intersects the curve. Draw a horizontal line from this point toward the left until it intersects the mass scale. Read the mass off the scale. It is approximately 0.8 kg, as shown in Fig. 7-3.
Fig. 7.3 . Solution to Problem 1.
What will the “mass meter” shown in Fig. 7-1 , and whose mass-versus-frequency function is graphed in Figs. 7-2 and 7-3 , do if a mass of only 0.000001 kg (that is, 1 milligram or 1 mg) is placed in between the springs?
The scale will oscillate at essentially the frequency corresponding to zero mass. This is off the graph scale in this example. You might be tempted at first to suppose that the oscillation frequency would be extremely high, but in fact, any practical “mass meter” will oscillate at a certain maximum frequency even with no mass placed in between the springs. This happens because the springs and the clamps themselves have mass.
Wouldn’t it be easier and more accurate in real life to program the mass-versus-frequency function into a computer instead of using graphs like the ones shown here? In this way, we could simply input frequency data into the computer and read the mass on the computer display.
Yes, such a method would be easier, and in a real-life situation, this is exactly what a physicist would do. In fact, we might expect the scale to have its own built-in microcomputer and a numerical display to tell us the mass directly.
Practice problems of these concepts can be found at: Mass, Force, And Motion Practice Test
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