Find Acceleration of Blocks A & B | Homework Statement

In summary, two blocks, A and B, are connected by a cord and resting on a horizontal plane. Block A starts from rest and moves to the left with constant acceleration. After moving a distance of 24 m, Block B attains a velocity of 12 m/s. The acceleration of Blocks A and B can be found using an equation that takes into account the fixed length of the cord and the anchor point on the floor. This equation can be derived using the derivative of position and velocity. By cutting the cord near the objects, the movements of the blocks can be separated and counted.
  • #1
mashac
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Homework Statement



Question:

2 Blocks A and B are resting on a horizontal plane and connected by a cord as shown in figure. The Block A starts from rest and moves to the left with constant acceleration.It was observed that the Block B attains a velocity of 12 m/s after moving a distance of 24 m.
Find acceleration of Blocks A & B.


http://img862.imageshack.us/img862/9556/0806201127481.jpg

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Homework Equations





The Attempt at a Solution




In the solution there is an equation 3*accel of B+2*accel of A=0. I didn't understand this equation and the reason for using it. Is it a special property of cord? .I know how to find accel of Block B but to find accel of Block A this equation is used. Please, explain me about this equation and in what situations it is used.
 
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  • #2


Note that the cord is of a fixed total length. Also note that the cord is anchored at a fixed location on the "floor". If you set up your coordinate system so that this anchor point is the origin, then you can, using the fact that the cord length is fixed, derive a relationship between the position of block A and the position of block B.

The derivative of position is velocity. The derivative of velocity is acceleration. Your mystery relationship will pop out of the process.
 
  • #3


You can "cut" the cord near the object, and this will give you a divider for its movements.
Counting the way the red line cuts the cord near the objects.

[PLAIN]http://img23.imageshack.us/img23/8681/pulleyc.jpg
 
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FAQ: Find Acceleration of Blocks A & B | Homework Statement

1. What is the purpose of finding the acceleration of blocks A and B?

The purpose of finding the acceleration of blocks A and B is to understand the motion of these objects and how they interact with each other. Acceleration is a measure of how quickly the velocity of an object changes, and by finding the acceleration of these blocks, we can determine the forces acting on them and predict their future motion.

2. How do you calculate the acceleration of blocks A and B?

The acceleration of blocks A and B can be calculated using the formula a = (v - u) / t, where a is the acceleration, v is the final velocity, u is the initial velocity, and t is the time taken. We can also use the formula a = F / m, where F is the net force acting on the blocks and m is their mass.

3. What information do you need to find the acceleration of blocks A and B?

To find the acceleration of blocks A and B, we need to know the mass of each block, the net force acting on them, and the initial and final velocities. We also need to know the time taken for the motion to occur.

4. What factors can affect the acceleration of blocks A and B?

The acceleration of blocks A and B can be affected by various factors such as the net force acting on them, their mass, and the surface they are on. Friction and air resistance can also impact the acceleration of these blocks.

5. Why is it important to find the acceleration of blocks A and B?

It is important to find the acceleration of blocks A and B because it allows us to understand the motion of these objects and make predictions about their future motion. It also helps us to analyze and determine the forces acting on the blocks, which can be useful in various scientific and engineering applications.

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