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What is Mass and Force Help

By — McGraw-Hill Professional
Updated on Oct 25, 2011

Introduction to Mass and Force

What are you really doing when you drive a 2-ton vehicle down the Interstate at high speed? Why does your suburban utility vehicle try to go off the road if you take a curve too fast? Why should you never drive a pickup truck full of loose, heavy bricks? In this section, we’ll take a close look at the “why and wherefore” behind how things move, and what they can do when they move.

Mass

The term mass refers to sheer quantity of matter, in terms of its ability to resist motion when acted upon 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.

Mass is a Scalar

The mass of an object or particle has magnitude (size or extent), but not direction. The mass of any object can be quantified in units such as kilograms (kg). Mass is customarily denoted by the lowercase italic letter m.

You might think that mass can have direction. When you stand somewhere, your body presses downward on the floor or the pavement or the ground. If someone is more massive than you, his 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 pressing-down or pressing-back 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. It’s like temperature or sound intensity. Mass is a scalar quantity because it can be expressed by a plain, ordinary number.

How Mass is Determined

The simplest way to determine the mass of an object is to measure it with a scale. But 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. This field has about the same intensity, no matter where you go on the planet. But it’s different on the moon or on other planets. The mass of a 1-kg bag of dried peas is the same wherever you take it on earth. But it will weigh less on the moon, because the moon’s gravitational field is weaker.

Let’s conduct a little thought experiment. Suppose you are on an interplanetary journey, coasting along on your way to Mars, and everything in your space vessel is weightless. How can you measure the mass of an object, such as 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. 15-1). If you put something between the springs and pull it to one side, the object oscillates, or “see-saws.” You try this with a pea, and it “see-saws” rapidly. You try it again with a lead shot, and the springs oscillate slowly. This mass meter is anchored to a wall in the space ship’s cabin. (Anchoring the mass meter keeps it from wagging back and forth in mid-air after you start an object oscillating against the springs.)

How Things Move HOW MASS IS DETERMINED

Fig. 15-1. Mass can be measured by getting an object to “see-saw” between a pair of springs in a weightless environment.

A scale of this type must be calibrated in advance before it can render meaningful figures for masses of objects. The calibration can be shown as a graph of the oscillation period (the time it takes for the object to complete one cycle of “see-saw” motion) or oscillation frequency (the number of complete “see-saw” cycles per second) as a function of the mass. Once this calibration is done in a weightless environment and the graph has been drawn, you can use the spring device and the graph to measure the mass of anything within reason. The readings will be thrown off if you try to use the mass meter on earth, on the moon, or on 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.

Find practice problems and solutions at What is Mass and Force Practice Problems.

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