Acceleration of block/pulley system

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SUMMARY

The acceleration of the 2.0 kg block (Block B) in a block/pulley system is half that of the 1.0 kg block (Block A) due to the constraints of the pulley mechanism. The tension in the string remains constant across both blocks, leading to differing accelerations. Specifically, if Block A accelerates at 'a', Block B will accelerate at 'a/2'. This relationship is critical for solving problems involving connected masses in a frictionless environment.

PREREQUISITES
  • Understanding Newton's Second Law (F=ma)
  • Basic principles of pulley systems
  • Concept of tension in strings
  • Knowledge of acceleration constraints in connected systems
NEXT STEPS
  • Study the mechanics of pulley systems in detail
  • Learn about tension forces in multi-body systems
  • Explore advanced applications of Newton's laws in dynamics
  • Investigate real-world examples of block and pulley systems
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Students studying physics, particularly those focusing on mechanics, as well as educators looking for clear explanations of acceleration in pulley systems.

genevieveb
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Homework Statement


What is the acceleration of the 2.0 block in the figure across the frictionless table?
Hint: Think carefully about the acceleration constraint.
I've attached the diagram.

Homework Equations


F=ma


The Attempt at a Solution


A=1.0kg block
B=2.0kg block
For block A: mAa1=2T
0=-Fg+n
For block B: mBa2=T-Fg
and no forces in x direction

So I assume the tension is equal because it is the same string. I also assume that the accelerations are different for the blocks though I'm not completely sure what to assume/why. All I really need is an explanation as to what I should know about the acceleration and why that is.
 

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genevieveb said:

Homework Statement


What is the acceleration of the 2.0 block in the figure across the frictionless table?
Hint: Think carefully about the acceleration constraint.
I've attached the diagram.

Homework Equations


F=ma


The Attempt at a Solution


A=1.0kg block
B=2.0kg block
For block A: mAa1=2T
0=-Fg+n
For block B: mBa2=T-Fg
and no forces in x direction

So I assume the tension is equal because it is the same string. I also assume that the accelerations are different for the blocks though I'm not completely sure what to assume/why. All I really need is an explanation as to what I should know about the acceleration and why that is.

That pulley system means that B will move half as much as A. half the distance, half the speed, half the acceleration.
 
Oh okay, that makes sense. Thanks a lot!
 

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