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1G10.40 - Bicycle-Size Atwood's Machine

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​1G10.40 - Bicycle-Size Atwood's Machine

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Title1G10.40 - Bicycle-Size Atwood's Machine
Objective

The Atwood's Machine is a two body system that demonstrates the interdependence of forces on two masses connected by a string on a pulley.​

StatusAvailable
Assembly Instructions

The bicycle Atwood is set into a static condition where the equal masses are not in motion and are at equal heights above the floor.


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Setup Time10
Operation Time
Preview Time5
Operation Instructions

A small slotted mass is added to the balanced masses and the class observes an acceleration of the mass. If the equal masses are simply perturbed by a gentle push, the motion of both masses continues in a non accelerated condition.

ExportableNo
Demo on DimeNo
PIRA 200Yes
Export Instructions (if different)
HazardsNone
Analysis/Information

Analysis

Two masses connected by a "massless, inextensible" string on a pulley can reveal the subtle interplay of mass, acceleration and force. While experience prepares us to answer which way the pulley will spin if one mass is heavier than the other, characterizing the relationship between the acceleration of each mass, the force on each mass, and the tension of the string at different points is often challenging for students.

 
Acceleration:
The acceleration of an object is simply an observation of the rate of change of velocity of that object. Two masses connected by a string that cannot be streched will be displaced by the same distance, with the same velocity at any moment, and the same acceleration at any given moment. They are a bound system.
 

Tension:

The tension in a string is an often challenging example of Newton's Third Law. Students sometimes draw free-body diagrams with the force of the string at the more massive m2 junction as less than the force on the string at the m1 junction. They seem to be reconciling the motion of the system as a whole by characterizing the internal forces of the system in an unphysical way. If the forces on the string at either end are different, then the string would collapse or distend. Massless, inextensible string does not distend and does not collapse in the arrangement we present.

Here are some ways to think about a two body system connected by a rope. If two people are involved in an evenly matched tug-of-war (no one is moving), it doesn't matter if one person is larger than the other, they are exerting an equal force on the rope to make it taut and stationary. Now imagine that one person gets the upper hand and is able to move backward. The rope has the same level of tautness (so there are equal forces on each end of the rope), but is not stationary. The rope is moving at the same rate as the people toward the winners side.
 

If you cut the rope mid-game the winner's rope will fly back faster than the losers, but this is not because the tension in the string is unequal and greater toward the winner (as the loser might claim or unequal arrows in a force diagram would indicate), it is because of the winners superior strength. If the referee wanted to keep the game going (and fair) then the ref would jump in and hold each end of the cut rope with equal force. A fair rope is the same thing as a fair referee, it obeys Newton's Third Law, it does not apply an unequal force in opposite directions within the string.

 

Force:
The force on each mass is different if the masses are different. Less force is required to move a less massive object than a more massive object with the same acceleration. You will see this in your free body diagram. The tension of the string is the same at each mass, but the masses have different weights. The sum of the forces at each junction will be different, indicating different force on each mass. Same acceleration but different mass mandates the forces must be different on each block, so this model accurately describes the Atwoods machine.

Using these relationships, we can construct a series of equations that tell us the exact acceleration of the system due to gravity.

Concept Questions:
  1. Is the acceleration of the rising mass the same as of the falling mass?
  2. Is the force the same on the rising mass as on the falling mass?
  3. If a connected mass is falling, is it in free fall (i.e. a = g)?
  4. Is the tension in the string where it connects to m1 equal to where it connects to m2?
  5. Does the acceleration depend on the initial positions of the masses (if one is higher than the other)?

Analysis Links
L. C. McDermott, P. S. Shaffer, and M. D. Somers, "Research as a guide for teaching introductory mechanics: An illustration in the context of the Atwood's machine," Am. J. Phys. 62, 46–55 (1994)
​

Category1 Mechanics
Subcategory1G - Newton's Second Law
Keywordsuniform motion, uniform acceleration
Construction Information
 
Equipment TitleUse SHIFT+ENTER to open the menu (new window).
  
QuantityUse SHIFT+ENTER to open the menu (new window).
  
Atwood pulley bicycle wheel
1
string nylon
mass 1-kg hooked
2
mass 500-g hooked
2
mass 10-g slotted
2
tripod base - large
1
tripod base transport cart wooden
1