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Goals: The student will
- Learn to distinguish between weight and mass. Mass is really just another name for inertia. Both mass and weight are properties of matter, and all observations suggest that they are proportional to each other. Weight is the force by which an object is attracted by gravity. Mass is the extent to which it resists acceleration.
- Learn that in oscillations of a mass against an elastic spring--in the absence of gravity, or in horizontal motion--the length of the oscillation period is proportional to the square root of the mass. This makes it possible to compare masses without the use of gravity.
- Learn about space station Skylab and the measurement of astronaut mass conducted aboard it.
Terms: mass, weight, inertia, zero-g
Stories and extras: The story of Skylab and studies of weight-loss by its crew members.
Hands-on activities: A simple experiment with a clamped hacksaw blade, containing some elements of the Skylab measurements.
Notes to the teacher:
- These linked sections are relatively free of mathematics, because they stress the intuitive distinction between weight and mass, a subject on which many students and even some teachers are unclear. It is hoped that the distinction is made clear by approaching it in more than one way, and illustrating it by as many examples as possible.
- Some teachers still maintain that a two-pan balance measures weight, while a spring balance measures mass. This is misleading and should be avoided: both devices rely on gravity, and therefore both measure weight.
The way they do so differs. The two-pan balance compares the weight of the object being examined to that of a set of standard weights in the other pan. The spring balance, on the other hand, compares that weight to the pull of a calibrated spring.
Thus on the Moon, where gravity is only 1/6 of its value on Earth, the spring balance will record a smaller weight, but the two-pan balance will not. That is because on the Moon, the pull of the spring is unchanged, but the balancing weights in the other pan also weigh only 1/6 of what they weigh on Earth. In both cases, however, what is measured is weight, not mass, because gravity is involved.
Starting out: Today we return to two concepts already discussed in a previous lesson--weight and mass. They often get confused! Since both are measured in kilograms or pounds, many students (even some teachers) feel both represent the same thing.
(Write the following on the board)
(End of words copied from the board)
Galileo showed by experiments that (disregarding air resistance) big stones fell no faster than small ones. Newton asked himself: why? If they were pulled down by a stronger force, why didn't they fall any faster?
He guessed the reason. All material also resists acceleration. A big stone with 10 times the weight of a small one also has 10 times the resistance, and therefore it does not fall any faster. Newton named the resistance to acceleration intertia. We call it mass.
If the only use of the concept of mass was for explaining why big and small stones, in free fall, accelerated at the same rate, it would not be very useful. However, there also exist many motions in which gravity plays no role--horizontal motions on Earth, and motions in "zero g" in space. Weight does not drive such motions, but inertia remains an important factor.
For instance...
Continue with examples from the lesson, of a rolling bowling ball and a rolling wagon--both starting their motion and stopping it.
Examples already mentioned: we read about train locomotives hitting cars which stalled on railroad tracks, because those trains were too massive to stop quickly.
Supertankers (aka "large crude oil carriers"), ships of 200,000 tons and more, are even harder to stop when fully loaded, taking several miles to do so.
[This is probably no longer topical, relating to matrix printers, widely used in the 1980s, before laser printer and ink-jet printers entered wide use. They used tiny metal slugs which pushed an inked ribbon against the paper output from a computer. The slugs were arranged in an array (matrix) and depending on which of them were pushed (by magnets), letters and symbols were formed. They are still used in industry to mark boxes. The slugs had to be tiny and very light, so they could hit and rebound very rapidly.]
Then go over Skylab story. As a project, some students may prepare a presentation on Skylab, based on the October 1974 article about it in "National Geographic." All past issues of that magazine are available on compact disks, or in paper copies in libraries.
The hands-on experiment in section (17b) may be performed as the teacher chooses--together with the Skylab discussion, before it or afterwards.
Guiding questions and additional tidbits with suggested answers.
-- What is the difference between the mass and weight of a bowling ball?
The ball has both weight and mass. Its weight makes it hard to lift. Its mass makes it hard to get rolling, and also hard to stop.
--What do we mean by the ball's weight?
Its weight is the force by which gravity pulls the ball down.
-- What do we mean by the ball's mass?
The ball's mass is its inertia, its resistance to acceleration.
-- Suppose that some time, in the far future, a bowling alley is built on the Moon, where gravity is 1/6 of what it is on Earth. Would it be easier there to roll the ball down the alley?
It would be easier to lift the ball off the floor, but not any easier to get it rolling.
--An astronaut in a space suit, in the space shuttle bay, tries to push a one-ton scientific satellite out of the bay, but the satellite proves very hard to move. If it is weightless, why should it be so?
In the moving frame of reference of the space shuttle, it has no weight, but it has one ton of mass.
--Should the astronaut give up trying to push it?
Not necessarily. If he keeps pushing it will accelerate--it just does so very slowly. In a minute it might be moving fast enough to float out of the bay. At this point, however, the astronaut better be ready to let it float away--trying to stop it would be just as hard!
--On Earth we drop from a high point a bowling ball and a marble. The marble has only 1/1000 of the weight of the ball, but it falls just as fast. Why?
The marble also has only 1/1000 of the inertia or mass of the bowling ball. By Newton's law
a = F/m
Both F and m for the marble are 1/1000 times less, but their ratio is the same as with the bowling ball, and therefore the marble accelerates at the same rate.
--If the Earth's gravity reaches up to the Moon (which is held by it), how can we have a "zero gravity" environment aboard a space station that orbits a mere 300 miles above ground?
Gravity does act on the space station, too--that is what keeps it in its orbit. In fact, gravity is the
only external force acting on it and on the astronauts inside (same as it is in free fall).
That means that inside the station, no additional force pulls objects towards Earth. In the reference frame of the space station it feels like "zero g", because no outside force is evident. ["Stargazers" returns to this matter in a later section, where frames of reference are discussed.]
--Before electronic wrist-watches were introduced (around 1980), mechanical ones were used. How were they designed, to operate in any position?
They obviously could not depend on gravity, so they too used a spring and an oscillating mass. The mass was a balance wheel, which rotated back-and-forth against a spiral spring.
[It might be possible to show the class an old mechanical alarm clock with its back removed, provided the balance wheel is clearly visible, which often is not the case.]
(Questions about the "Skylab" section, #17a)
--How can mass be measured in "zero g"?
--How was astronaut mass measured aboard Skylab?
--What did measurements of astronaut mass aboard Skylab reveal?
(Question after the experiment in section #17b)
-- Suppose the same hacksaw blade described in the author's experiment in section #17b was also used in the mass-measuring device aboard Skylab. If the device carried an astronaut known to weigh about 70 kg, what would be its back-and-forth period?
In the notation of that section, for m1 = 50 gr., the blade gave a period T1 of 0.5 seconds. If m2 = 70 kg, m2/m1 = 1400, SQRT(m2/m1) = 37.42, multiply by T1 = 0.5 sec to give T2 ~ 18.7 seconds.
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