Download Rubber Band newton Scale

Rubber Band newton Scale
It's not a mistake! -- it really is newton, not Newton
When you weigh something with a spring scale, you are really measuring the force of
gravity on the object. In the metric, or SI System, of units (see discussion in the What's
Going On section below), force is measured in newtons (with a small n). The abbreviation for
newton is N. One newton is roughly equal to 1/4 pound in our everyday measuring system -a McDonald's "Quarter Pounder" could therefore reasonably be called a "One newtoner!"
Materials
~ 5 in
• cardboard or mat board, 4 in x 12 in
• 3 brass fasteners, 1 1/2 in
• rubber band (#19 works well)
• single hole paper punch
• 1 regular paper clip
• string (approximately 1 ft)
• 2 jumbo paper clips
• marker pen
• calibration weights: -- 500 mL water bottles are ubiquitous, and can be filled with the
appropriate amount of water to make a set of calibration weights in the 1-5 N range -- keeping in
mind that a mass of 100 grams weighs approximately 1 N here on earth (see What's Going On
section below for background discussion), that water has a density of 1g/mL, and that a random
empty 500 mL water bottle and cap weighed at this writing was 16 grams, we find that a bottle &
cap + 34 mL of water weighs 0.5 N, bottle & cap + 84 mL of water weighs 1.0 N, etc. -- a brass
cup hook screwed into the lid allows the bottle to be conveniently hung -- the appropriate amount
of water can be added by volume, using a graduated cylinder, or by mass, using a balance -alternatively, items of known mass (e.g., steel washers) can be used for calibration weights
Assembly
Use the materials listed to make the scale shown in the photo.
Use calibration weights to calibrate the scale from 0 to approximately 3 N, in steps of 0.5 N. Be
aware that the rubber band may not be "linear" in its stretch -- that is, the calibration marks may
not be evenly spaced. Label the calibration marks with their values.
(If you want to recalibrate at some point, just cover the original marks with masking tape, and
write the new values on the masking tape.)
To Do and Notice
Weigh different objects with the calibrated scale. This will help give a feel for the newton (N) as a
unit of force. Some examples of common items that might be weighed are a D-cell battery, an
apple, a coffee cup, etc. If the object cannot be hung conveniently, try sticking a masking tape loop to the object.
Notes, Comments and Tips
Rubber bands have a limited useful lifetime. Your calibration marks may change somewhat with repeated stretching, or if the rubber
band is overstretched. Over longer periods of time the rubber band will likely degrade and break, even if not used. You can use
other rubber bands that are shorter, longer, lighter, heavier, etc. (e.g., if you want to measure larger weights, use a heavier rubber
band -- or use two rubber bands side by side). The balance will have to be recalibrated if the rubber band is changed.
What's Going On
The SI Unit system (Le System International d'Unites) is based on certain fundamental units. Where force and motion are
concerned, these fundamental units are the meter, kilogram and second (sometimes this is called the mks system of units). All other
quantities dealing with force and motion, such as force, velocity, acceleration, energy, etc., are called derived units, and can be
expressed as some combination of the three fundamental units, meter (m), kilogram (kg) and second (s).
Newton's 2nd Law states that Force = Mass x Acceleration, or F = ma. Suppose we give a 1 kg mass an acceleration of 1
2
m/s/s (commonly expressed as 1 m/s ) -- then
2
2
F = 1 kg x 1m/s = 1 kg m/s = 1 N
2
Notice that for force the fundamental units are kg m/s -- the official SI force unit, representing this combination of
2
fundamental units, is the newton (N).The force necessary to give a 1 kg mass an acceleration of 1 m/s is 1 N.
We know that here on earth, all objects falling under the influence of gravity alone (i.e., air resistance considered negligible)
2
fall with the same acceleration, 9.8 m/s/s, or 9.8 m/s . If we apply Newton's 2nd Law to the case of free fall, we can express it as
W = mg, where W is the force of gravity on the object (in other words, its weight), m is the mass of the object, and g the gravitational
2
2
acceleration (9.8 m/s/s). If we use a mass of 1 kg, then W = mg becomes W = 1 kg x 9.8 m/s = 9.8 kg m/s ~ 10 N. So for
convenience, we can say that a 1 kg mass here on earth has a weight of approximately 10 N. Generalizing (and again
approximating), if you multiply a mass in kg by 10, you will get the weight in N, here on earth.
Referring back to the Materials section, it was noted that a 100 g mass weighs approximately 1 N. 100 g = 0.1 kg, and
multiplying this by 10 as just noted, we get 1 N. (More exactly, 100 g weighs 0.98 N, and 102 g weighs 1.0 N.)
Rubber Band Scale.....4/10/09
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Don Rathjen....Exploratorium Teacher Institute....3601 Lyon St., San Francisco, CA [email protected]
© 2009 Exploratorium, www.exploratorium.edu