Constraint Relations: Acclerations of Blocks in System

In summary, the conversation is about the relation between the accelerations of each block in a system shown in a picture. The person asking the question is unsure of their calculations and wants to confirm the accelerations of each block. They mention that if the middle block moves up by x, the string will get loose by 2x and the relation between the accelerations is -2*a2=a1+a3. The other person confirms that this sounds correct, but the person asking the question realizes they made a mistake with the signs in their calculations. They ask for the accelerations to be directly stated so they can compare with their own calculations.
  • #1
ritwik06
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0
The system is given in the picture. I want to know the relation between the acclerations of each block.

My attempt:
suppose if the body in the middle moves up by x. the string will get loose by 2x. therefore, if a1, a2, a3 are the acclerations. -2*a2=a1+a3
am i correct?
 

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  • #2
Sounds right to me.
 
  • #3
But the thing is that my calculated accelerations of the three blocks differ from the answer in my book. Can you please just tell me the acclerations of each block? (in order that I may know if I am right)
 
  • #4
Show what you did and I'll check it out.
 
  • #5
Thanks for the help. I actaully was solving with the wrong sign.
 

FAQ: Constraint Relations: Acclerations of Blocks in System

What are constraint relations?

Constraint relations are mathematical equations that describe the relationships between the accelerations of blocks within a system. They are used to analyze the motion of objects in a system and determine how they are affected by external forces.

How are constraint relations used?

Constraint relations are used to solve problems involving the motion of multiple objects in a system. By applying Newton's second law and using the constraint relations, we can determine the accelerations of each block in the system and how they are related to each other.

What is the difference between holonomic and non-holonomic constraints?

Holonomic constraints are equations that relate the positions and velocities of objects in a system, while non-holonomic constraints also involve the accelerations of these objects. Non-holonomic constraints are more complex and require additional equations to solve.

How do you determine the degrees of freedom in a system?

The degrees of freedom in a system are determined by the number of independent variables needed to describe the motion of all the objects in the system. For example, a system with two blocks connected by a string has two degrees of freedom.

Can constraint relations be used to analyze systems with more than two blocks?

Yes, constraint relations can be used to analyze systems with any number of blocks. However, as the number of blocks increases, the complexity of the equations and calculations also increases, making the analysis more challenging.

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