Struggling with constrained motion of connected particles

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SUMMARY

The discussion centers on solving a physics problem involving constrained motion of connected particles, specifically calculating the velocities of two particles, A and B, given their geometric relationships and constraints. The user sets the origin at the bottom right and uses trigonometric functions and the Pythagorean theorem to derive the velocities. Despite calculating a velocity for particle B as 7.745 m/s and a total speed of 8.944 m/s, the user finds a discrepancy with the book's answer of 2.76 m/s, indicating a miscalculation in their approach. The community suggests reviewing the relevant equations for accuracy.

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  • Understanding of trigonometric functions, specifically cosine and sine.
  • Familiarity with the Pythagorean theorem and its application in physics problems.
  • Basic knowledge of calculus, particularly differentiation in the context of motion.
  • Ability to interpret and manipulate equations related to velocity and acceleration.
NEXT STEPS
  • Review the principles of constrained motion in physics.
  • Study the application of the Pythagorean theorem in two-dimensional motion problems.
  • Learn about differentiating equations in the context of motion to find relationships between velocities.
  • Examine examples of similar physics problems to identify common pitfalls and correct methodologies.
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Students studying physics, particularly those focusing on mechanics and motion, as well as educators looking for examples of problem-solving in constrained motion scenarios.

Imperiosus
Hi everyone!

Really struggling with this question here, was hoping someone could point me in the right direction?
https://puu.sh/xVitw/4c0b89c576.png

1. Homework Statement

Set origin to bottom right.
OA is y (Which using cos(60)*R you can determine to be 0.5R).
OB is x (which you can determine using Pythagorean (2R)^2 = (0.5R)^2 + x^2 x =sqrt(3.75).
We are told in the problem that the speed of b is 2m/s.

Homework Equations


[/B]
L^2 = x^2 + y^2
Differentiate everything Note a=velocity of x and b = velocity of y in the y direction
0= 2xa + 2yb

The Attempt at a Solution


We know the velocity of x is 2
0= 2(sqrt3.75)(2) + 2(0.5)(b)

b=7.745 and using trig i get 8.944 for the speed of y total. (7.745/sin60)

According to the back of the book, the answer is 2.76, so clearly I am doing something very wrong!

Any help is appreciated, Thanks!
 
Last edited by a moderator:
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Check your relevant equations. The first one is not correct.
 

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