Follow

LecDem Blog

Atwood's Machine: Testing Newton’s Second Law

Atwood's Machine demonstration: identical masses hang stationary from a string looped over a lightweight pulley, next to a mounted meter stick Figure 1

Atwood’s Machine is a device initially developed by George Atwood in the 18th century as a way of testing Newton’s Laws mechanically. We have a three demonstrations of this device, C4-21: Atwood Machine, C4-22: Horizontal Atwood Machine, and C4-23: Atwood Machine with Heavy Pulley which can be used in the classroom to measure the acceleration of masses under gravity.

 At its simplest, Atwood’s Machine is a pulley with a string over it, with an object hanging on each end of the string, pulled down by gravity. According to Newton’s Laws, the force on each end of the string is dependent on the mass. In Atwood’s idealized, theoretical mathematical model of the experiment, the pulley and string themselves have no mass, so only the hanging objects’ mass we add affects the force.

So long as the masses are equal, there is the same force pulling down on each object – so there is no net force on the system. So if the two objects start out stationary, they remain stationary, by the principle of inertia. If they start out moving, they continue moving at the same speed (until they run out of string).

If one mass is greater than the other, then there are different forces acting on each end, so there is a net force on the system. This net force will cause the masses to accelerate. But this is where it gets complicated: the force on each end of the string from gravity is proportional to the mass on that end. But because the masses are tied together and transmit force to each other through the tension in the string, the acceleration is proportional to the net force and to the total mass of the system. But since each of the component forces is proportional to that mass, the final acceleration ends up being proportional to the ratio between the difference in masses and the total mass.

a=g(m1-m2)/(m1+m2)

 

You can also use this device another way – by timing how fast the objects accelerate, if you know their masses, then you can measure the force of gravity!

g=a(m1+m2)/(m1-m2)

In a real experiment, of course, the string and pulley very much do have mass. Additionally, there is another source of force on the system: the friction in the pulley. This frictional force acts to reduce the speed of the moving masses. Additionally, the force from gravity must move the mass of the rotating pulley as well as the mass of the hanging objects.

For one version of this demonstration (figure 1 above), we carefully chose a pulley with a very low mass, so it behaves very much like the theory predicts.

For the other (figure 2 below), we have a much heavier pulley. It has greater mass, and thus accelerating the hanging objects also means overcoming the pulley’s inertia as well.

Atwood's machine demonstration: weighted strings hang over both a light pulley and a heavy pullet Figure 2

This is an important aspect of the difference between theory, simulation, and experiment, and valuable to talk about in class. In a theoretical model, we can propose things that don’t really exist in the real world – massless strings, frictionless pulleys, objects of constant mass but zero size. We use these theoretical experiments to test out theories mathematically, to see if our theories will give results that make sense, and to plan an experiment.

With a real experiment, there are more variables we have to take into account that can affect the results – friction, inertia, heat, objects that stretch and swing and wear down over time. But it’ is these real-world experiments that let us take that final step and ensure that our theories accurately predict the outcome of real-world physics.

 A simulation is somewhere in between the two. We can simulate a physics experiment inside a computer, as another way of testing our theories. This has its own limitations, since the computer only knows about the laws of physics we program into it – if our initial assumptions are wrong or if we set them up incorrectly, the simulation may give inaccurate results. But the simulation lets us try out many combinations of factors in succession, making tiny changes each time, in ways we might not be able to in the laboratory. It’s much faster to adjust a measurement in a simulation than it is to build a new device on the workbench.

 And, importantly, we can use a simulation to practice an experiment when we can’t get to the laboratory at all!

 This simulation, by Andrew Duffy of Boston University, lets us try out the Atwood Machine at home on our computers, or on the screen in the classroom http://physics.bu.edu/~duffy/HTML5/Atwoods_machine.html 

We can vary the mass of each of the two hanging objects, from 0.1 kilograms (100 grams, about the mass of a small bar of soap) to 2 kilograms (2,000 grams, close to the mass of a 5-pound bag of flour). You can set the masses and then start the simulation running, and it will measure the forces and acceleration as it runs. Try it out and see if you can replicate our demonstration, then experiment and test its limits!

 

More Articles ...

  1. STEM News Tip: Some new articles in science teaching & information, August 2020
  2. Demonstration Highlight: Masses Dropped and Shot
  3. STEM News Tip: Native American Physics & Astronomy
  4. STEM News Tip: Titan and its Atmosphere on APOD
  5. STEM News Tip: COVID-19 impact on research
  6. The Tablecloth, the Coin, and Other Adventures with Inertia
  7. Quantum Demonstration and Simulation: The Hydrogen Atom
  8. STEM News Tip: New Atmospheric Phenomena Spotted on Venus
  9. STEM News Tip: SPS Virtual Colloquium
  10. Demonstration Highlight: Simple Harmonic Motion & Uniform Circular Motion
  11. STEM News Tip: Meteor Showers and Rain Showers
  12. STEM News Tip: Sonic Tourism
  13. Demonstration Highlight: Electromagnet
  14. STEM News Tip: Mars 2020 launches this week!
  15. STEM News Tip: Nova Reticuli 2020
  16. How many demonstrations?
  17. STEM News Tip: Solar Observer webcast this week!
  18. STEM News Tip: Children Learning About Gears
  19. Space News: The Nancy Grace Roman Space Telescope
  20. Demo Highlight: Vector Addition
  21. Demonstration Highlight: The Pencil and Plywood Experiment
  22. Demo Highlight: The Ripple Tank and a Ripple Tank Simulator
  23. Demo Highlight: The Racing Balls in Slow Motion
  24. Happy birthday, Alexander Müller
  25. New Demonstration: The Paramagnetism of a Dysprosium Pendulum
  26. Welcome to Spring 2020
  27. Light Up the Night: Neon and "Neon" Lights
  28. A Heated Discussion In Class
  29. The Physics Soda Can Returns: Electrostatic Induction
  30. Physics Teatime 3: Do Not Try This At Home
  31. Introducing Our Newest Center of Mass Demonstration
  32. FLIGHT!
  33. Happy Birthday Carl Sagan
  34. Hot Air Balloon
  35. Upcoming Events at UMD Physics!
  36. Welcome to Fall 2019!
  37. Summer Hiatus
  38. Phun with Electrons: Particle or Wave?
  39. Physics Teatime 2: On The Making Of Tea
  40. On the Choosing of Demonstrations
  41. Teatime in Physics
  42. Happy Birthday to Émilie du Châtelet
  43. Seeing Sound: Vibrations on a Plate
  44. Women Nobel Laureates in Physics
  45. Coming Soon: Physics is Phun presents Induction and Deduction
  46. New Portable Ripple Tank
  47. Irene Joliot-Curie
  48. New Demos: Buoyancy and Electromagnetic Forces
  49. Falling into Free Fall
  50. Happy 100th Birthday Katherine Johnson!
  51. Demonstration Orders for the Fall Semester
  52. Welcome!