What Is the Acceleration in a Frictionless Pulley System with Varying Masses?

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SUMMARY

The acceleration of a frictionless pulley system with varying masses can be determined using Newton's second law. For the given masses in scenarios (a) m1=0.25kg, m2=0.50kg, m3=0.25kg and (b) m1=0.35kg, m2=0.15kg, and m3=0.50kg, the net force must be calculated considering both gravitational forces and tension in the strings. A free body diagram for each mass is essential to visualize the forces acting on the system. This approach leads to a system of equations that can be solved for the acceleration.

PREREQUISITES
  • Understanding of Newton's second law (F=ma)
  • Ability to draw and interpret free body diagrams
  • Knowledge of gravitational force calculations (F=mg)
  • Familiarity with systems of equations in physics
NEXT STEPS
  • Study the application of Newton's second law in multi-mass systems
  • Learn how to construct and analyze free body diagrams
  • Explore the concept of tension in pulley systems
  • Investigate examples of frictionless pulley problems in physics textbooks
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Students studying physics, particularly those focusing on mechanics, as well as educators looking for effective methods to teach concepts related to forces and motion in pulley systems.

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Homework Statement


Assuming ideal frictionless conditions what is the acceleration of the system if (a)m1=.25kg, m2=.50kg, and m3=.25kg and (b)m1=.35kg, m2=.15kg, and m3=.50kg. This is a picture of a table with m3 on the table, m1 and m2 hanging on the sides.


Homework Equations


a=Fnet/m
Fnet=ma


The Attempt at a Solution


I did a=Fnet/m=9.8N/m1+m2+m3=9.8m/s
The Fnet's (ma) for a and b both totaled 9.8N. I'm not sure.
 
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9.8 N is not Fnet. There are forces acting in more than one direction here. You must consider the tensions in the strings connecting the masses in addition to gravity. Draw a free body diagram of each mass, labelling all of the forces. Then use Newton's second law to sum up the forces in each direction for each mass. This will give you a system of equations to work with to solve for acceleration.

See http://hyperphysics.phy-astr.gsu.edu/hbase/hpul.html#c1 for examples using Newton's second law.
 

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