Struggling with constrained motion of connected particles

The second one should be x^2 + (0.5R)^2 = (2R)^2. The correct answer is 2.76In summary, the conversation discusses a problem involving determining the speed of an object, given its position and velocity in the x and y directions. The relevant equations are given, and an attempt at a solution is made, but the answer does not match the solution in the back of the book. The error is identified and the correct answer is provided.
  • #1
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!
 
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  • #2
Check your relevant equations. The first one is not correct.
 

FAQ: Struggling with constrained motion of connected particles

1. What is constrained motion in the context of connected particles?

Constrained motion refers to the movement of interconnected particles that are restricted in their motion by some external force or condition. This can include particles connected by rigid or flexible structures, such as a rod or a string, or particles constrained by a fixed boundary.

2. Why is understanding constrained motion of connected particles important?

Understanding constrained motion is important in various fields of science and engineering, such as mechanics, physics, and biomechanics. It helps us analyze and predict the behavior of interconnected systems, such as mechanical linkages, molecular structures, and biological tissues.

3. What are some common methods for studying constrained motion of connected particles?

Some common methods for studying constrained motion include analytical techniques, such as Lagrangian mechanics and Newton's laws of motion, and numerical simulations, such as finite element analysis and molecular dynamics simulations. Experimental methods, such as motion tracking and force measurements, can also be used to study constrained motion.

4. What are some challenges in studying constrained motion of connected particles?

One of the main challenges in studying constrained motion is accurately modeling and representing the complex interactions between connected particles. This requires considering factors such as the geometry, material properties, and external forces acting on the particles. Another challenge is solving the equations of motion for interconnected systems, which can be computationally intensive.

5. What are some real-world applications of studying constrained motion of connected particles?

The study of constrained motion has many real-world applications, such as designing and optimizing mechanical linkages in machines, understanding the movement of molecules and proteins in biological systems, and predicting the behavior of materials under stress and strain. It also has practical applications in fields such as robotics, biomechanics, and structural engineering.

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