Physics

9th - 12th grade

45 minutes

• The definition of period (the time it takes to complete one cycle)
• How to plot data using Excel or a similar program

The students will determine for themselves the relationship between mass and period of oscillation in simple harmonic motion. Further, they will use this relationship as a way to measure unknown masses.

Each group of 2-3 students will need:

• a stopwatch
• a spring of appropriate tension
• a ring stand
• plenty of known masses (50 g, 100 g, etc.)
• acess to a computer graphing software, such as Excel

And you will need 3 "unknown" masses (everyday objects with masses lying somewhere within or near the range of known masses you'll be giving them). Mr. Long has for years chosen to use a stuffed monkey, and the students typically get quite a kick out of watching it oscillate back and forth on the spring.

Procedure

Opener

Begin by showing the students the 3 unknown masses, and telling them that their challenge will be to determine the mass of these objects as accurately as possible by the end of the period. But there's a catch: they're not allowed to use a scale of any kind; in fact, catching them doing so should result in an immediate failing grade on this activity.

Ask them if they have any ideas as to how they could measure mass without a scale or a balance.

Development

The students should explore the relationship between the period of oscillation of a spring and the mass attached to its end. The experimental details can be left largely up to each group to decide for themselves, but the basic setup should involve the spring hanging vertically from the ring stand with the students attaching the masses to the end, displacing the spring from equilibrium, and observing the ensuing oscillation. Encourage them to measure multiple periods with the stopwatch to decrease measurement error, and suggest that they use more than 10 (and ideally 20 or more) different known masses to get lots of data points.

Whenever each group feels they are ready, they can ask you for the unknown masses. Some students may naturally graph their data, use Excel to find a line of best fit, and look at where the unknown masses fall on the best fit line for their measurement. Others may measure the period of oscillation with an unknown mass and then try to find a combination of known masses that matches this period. This provides a good chance to talk about which approach is more scientific and likely to be more accurate.

A significant portion of the lab grade should be based upon how accurately the students are able to mass the unknown objects.

In addition, here is a handout to give them for homework that emphasizes the ideas covered in the lab, placed specifically in the context of nanotechnology, which is a field currently using this exact idea in real application.

In what real world situations might it be necessary to measure a mass that can't be placed on a scale? Here are a few that come to mind:

• An individual biological molecule is far too small to mass on a scale. As discussed in the homework handout, nano-oscillators could provide a means of massing such molecules, and hence represent a possible way of diagnosing different diseases (which might be characterized by molecules of distinctive masses).
• Astronauts cannot mass themselves with a scale, as the lack of gravity prevents them from using one. Instead, astronauts sit in a special chair which is set into simple harmonic motion, and the period of the motion is a way of measuring the astronaut's mass.
• How have scientists estimated the mass of the planets in our solar system? Although planetary orbit around the sun is not simple harmonic motion, the period of each orbit certainly relates to the mass of the planet.

Here are a few articles discussing the use of nanotechnology as an ultrasensitive mass measurement:

Cornell Researchers Move Beyond 'Nano' to 'Atto'

Cornell NEMS Device Detects The Mass Of A Single DNA Molecule