How to calculate acceleration in this Atwood's Machine?

In summary, the conversation discusses finding the acceleration of block B using the equation (300-3T) and the tension in the string, and comparing it to the acceleration of block A which is found to be 2T. The correct answer is 1.56, but the original answer calculated was 1.71. The conversation concludes with a clarification that the accelerations of A and B are different due to the string constraint.
  • #1
ArnavVarshney
3
1
Homework Statement
Question: https://i.stack.imgur.com/xYp18.jpg

It asks us to find the acceleration of block B.
Relevant Equations
String constraint?
I concluded the net force on block B would be (300-3T) where T is the tension in the string and similarly, on block A it would be 2T. However, the answer I get (1.71) is incorrect. The correct answer is 1.56.
Could someone guide me to the solution of the question.
Sincere Thanks!
 
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  • #2
Show us your calculations to be able to tell you what you did wrong.
 
  • #3
ArnavVarshney said:
Problem Statement: Question: https://i.stack.imgur.com/xYp18.jpg

It asks us to find the acceleration of block B.
Relevant Equations: String constraint?

I concluded the net force on block B would be (300-3T) where T is the tension in the string and similarly, on block A it would be 2T. However, the answer I get (1.71) is incorrect. The correct answer is 1.56.
Could someone guide me to the solution of the question.
Sincere Thanks!
How does the acceleration of A compare to the acceleration of B?
 
  • #4
Chestermiller said:
How does the acceleration of A compare to the acceleration of B?
By string constraint, work done by tension would be zero. So, -3T(aB) + 2T(aA) = 0.
2aA = 3aB?
 
  • #5
Chestermiller said:
How does the acceleration of A compare to the acceleration of B?
Done! Thanks a lot! Was missing out on the fact that the two would have different accelerations!
 
  • Like
Likes Chestermiller

1. How do I find the acceleration in this Atwood's Machine?

To calculate the acceleration in an Atwood's Machine, you need to first determine the mass of each object and the tension in the connecting string. Then, use the formula a = (m1 - m2)g / (m1 + m2), where m1 and m2 are the masses and g is the acceleration due to gravity (9.8 m/s²).

2. What is the purpose of using an Atwood's Machine in experiments?

An Atwood's Machine is commonly used in physics experiments to demonstrate principles of motion and acceleration. It allows for the study of how two masses connected by a string move in relation to each other and how different variables, such as mass and tension, affect the acceleration of the system.

3. Can acceleration be negative in an Atwood's Machine?

Yes, acceleration can be negative in an Atwood's Machine. This indicates that the system is accelerating in the opposite direction of the force of gravity. This can occur if the mass on one side of the machine is significantly larger than the other side.

4. How does the angle of the string affect the acceleration in an Atwood's Machine?

The angle of the string does not have a significant effect on the acceleration in an Atwood's Machine. As long as the string remains taut and the masses are not too heavy, the angle of the string will not significantly impact the acceleration of the system.

5. What factors can affect the accuracy of calculating acceleration in an Atwood's Machine?

There are a few factors that can affect the accuracy of calculating acceleration in an Atwood's Machine. These include friction in the pulley system, air resistance, and the precision of the measurements for mass and tension. It's important to minimize these factors as much as possible for more accurate results.

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