An Atlumber Machine is a simple physics laboratory device frequently used to demonstrate basic principles of dynamics and also acceleration. The machine typically involves a wheel, a string, and a device of masses. Keys to resolving Atwood Machine problems are recognizing that the pressure transmitted by a string or rope, well-known as tension, is continuous throughout the string, and picking a regular direction as positive. Let’s walk through an instance to show.
You are watching: Atwood machine special cases
Question: Two masses, m1 and also m2, are hanging by a massless string from a frictionmuch less pulley. If m1 is greater than m2, recognize the acceleration of the 2 masses once released from remainder.
Answer: First, identify a direction as positive. Due to the fact that you have the right to conveniently observe that m1 will accelerate downward and m2 will certainly acceleprice upward, given that m1 > m2, speak to the direction of movement roughly the pulley and dvery own towards m1 the positive y direction. Then, you have the right to create free body diagrams for both object m1 and also m2, as displayed below:
Using this diagram, compose Newton’s second Law equations for both objects, taking treatment to note the positive y direction:
Next, combine the equations and get rid of T by fixing for T in equation (2) and also substituting in for T in equation (1).
Finally, deal with for the acceleration of the system.
Alternately, you can treat both masses as part of the exact same device.
Drawing a daburned line around the mechanism, you deserve to directly create an correct Newton’s 2nd Law equation for the entire system.
See more: Topographic Map Worksheet Answer Key, Topographic Maps Worksheets & Teaching Resources
Note that if the string and also sheave were not massless, this trouble would certainly come to be substantially more involved.