Solve Two Connected Masses for Acceleration

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SUMMARY

The problem involves two connected masses, 1 kg and 3 kg, moving vertically over a massless pulley. The correct approach requires recognizing that both masses experience the same acceleration due to their connection via the string. The forces acting on the 3 kg mass are represented as ma - T, while the forces on the 1 kg mass are mg - T. The acceleration of the 1 kg mass can be determined by applying Newton's second law, F=ma, to both masses simultaneously.

PREREQUISITES
  • Understanding of Newton's second law (F=ma)
  • Knowledge of free body diagrams
  • Concept of tension in strings
  • Basic principles of gravitational force (W=mg)
NEXT STEPS
  • Calculate the acceleration of connected masses using F=ma
  • Explore the concept of tension in systems with pulleys
  • Study free body diagram techniques for multi-body systems
  • Learn about the effects of mass distribution on acceleration
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Students studying physics, particularly those focusing on mechanics, as well as educators looking for examples of connected mass problems in dynamics.

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Homework Statement



Two masses are tied together by a string over a massless pulley so that they can both move vertically. Their masses are 1 kg and 3 kg. What is the acceleration of the 1 kg mass?

Homework Equations



F=ma
W=mg

The Attempt at a Solution



I have the 3 kg mass's summation of forces as ma-T. (In my free body diagram, the 3kg mass is the one closest to the pulley.)

The 1 kg mass's summation of forces are mg-T.

I'm unsure if my diagram is correct and I don't know where to go from here.
 
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Hi Juggernaut06 ! Welcome to PF! :smile:
Juggernaut06 said:
Two masses are tied together by a string over a massless pulley so that they can both move vertically. Their masses are 1 kg and 3 kg. What is the acceleration of the 1 kg mass?
…
I have the 3 kg mass's summation of forces as ma-T. (In my free body diagram, the 3kg mass is the one closest to the pulley.)

The 1 kg mass's summation of forces are mg-T.

No, both wrong :redface: …

both masses have both a and mg.

And of course a is equal (and opposite) for both. :wink:
 

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