Two-Block Dynamics Problem: Determining Acceleration and Tension

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SUMMARY

The discussion focuses on solving a two-block dynamics problem involving Block A (100kg) and Block B (300kg) on a frictionless plane. The equations of motion are established using ΣF = ma, leading to relationships between the tensions (T1 and T2) and accelerations (ax and ay) of the blocks. The user initially calculated ax as 14.8 m/s² and ay as 7.3 m/s² but later acknowledged that the correct acceleration for ax is 8.4 m/s², indicating an error in their calculations. The relationship ax = 2ay was derived from the professor's hint, which is crucial for solving the problem.

PREREQUISITES
  • Understanding of Newton's second law (ΣF = ma)
  • Knowledge of constrained motion in dynamics
  • Familiarity with tension in ropes and pulleys
  • Ability to solve simultaneous equations
NEXT STEPS
  • Review the principles of constrained motion in dynamics
  • Learn how to derive relationships between accelerations in pulley systems
  • Practice solving problems involving multiple blocks and tensions
  • Explore error analysis techniques in physics calculations
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Students studying physics, particularly those focusing on mechanics, as well as educators looking for examples of dynamics problems involving tension and acceleration.

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Homework Statement


Assuming no friction is on the plane or the pulleys and the pulley and rope have negligible mass... Determine the acceleration of each block and the tension in each cord. Block A weighs 100kg, Block B weighs 300kg.
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Homework Equations


ΣF = ma
ma = 100kg
mb = 300kg

The Attempt at a Solution



ΣFx = max = T1 = 100ax
ΣFy = may = W - T2 = 2943kg - T2 = 300ay
T1=2T2

I know that I have the relationships right, but I don't know exactly how to extract them...
 
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What is the relationship between ax and ay? It is constrained motion, so you relate the two accelerations.
 
I think I solved it this way based off of what my professor drew on the board but I need some clarity because I'm not quite sure how this can be...
if we assume:

ax = 2ay
^My professor's hint

then we have 4 relations and 4 unknowns. So:

T1 = 2T2
100ax = 2[2943 - 300ay]
50ax = 2943 - 300ay
ax = 2ay
50*2ay = 2943 - 300ay
400ay = 2943

ay = 7.3m/s^2
ax = 14.8 m/s^2

**Edit**
This is an incorrect answer. The correct answer is 8.4m/s^2 for ax which means somewhere my answer is almost 2 times larger.
 
Last edited:

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