# Double Differentiation and Acceleration in a Four Pulley System

• rudransh verma
In summary, the conversation discusses the acceleration of block B, which can be obtained by differentiating the y displacement twice with respect to time t. The resulting acceleration is 1/2 m/s^2. However, the position of B in relation to A is not as simple, as demonstrated by a series of pulleys and their corresponding movements. This leads to a discussion on faulty logic and the need for experimentation or visual aids to understand the concept better.

#### rudransh verma

Gold Member
Homework Statement
The vertical displacement of block A in meters is ##y=\frac{t^2}4## where t is in sec. Calculate the downward acceleration of block B.
Relevant Equations
##F=ma##
We can differentiate twice the y displacement with respect to time t and get the acceleration of block B. $$a_B= \frac12 m/s^2$$.
But I don’t think it’s that simple.

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You think correctly
But at least you have the acceleration of A.
How is the position of B in relation to A ? (if A moves up 1 m, how much does B move?)

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BvU said:
You think correctly

BvU said:
How is the position of B in relation to A ? (if A moves up 1 m, how much does B move?)
Of course 1 m since all are connected with unstrechable ropes.

Your logic is faulty. Think again. Number the pulleys 1,2,3,4 left to right. If 1 goes up by 1 unit, 2 stays in position unchanged, 3 ... etc.

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BvU said:
Your logic is faulty. Think again. Number the pulleys 1,2,3,4 left to right. If 1 goes up by 1 unit, 2 stays in position unchanged, 3 ... etc.

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Oh like that!
1 goes up by 1 unit then 2 stays in place, 3 and 4 goes down by 1 unit.

2 correct
3 think again, perhaps do the experiment..., or make 2 drawings...

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## 1. What is double differentiation in a four pulley system?

Double differentiation in a four pulley system refers to the calculation of the second derivative of the velocity or acceleration of a system that involves four pulleys. It is used to analyze and understand the motion of the system.

## 2. How is double differentiation used to analyze a four pulley system?

Double differentiation is used to analyze a four pulley system by calculating the rates of change of the velocity or acceleration. This helps to determine the direction and magnitude of the forces acting on the system.

## 3. What is acceleration in a four pulley system?

Acceleration in a four pulley system refers to the rate of change of the velocity of the system. It is a measure of how quickly the speed of the system is changing.

## 4. How is acceleration calculated in a four pulley system?

Acceleration in a four pulley system can be calculated by taking the second derivative of the displacement function with respect to time. This will give the instantaneous acceleration at any given time.

## 5. What is the relationship between double differentiation and acceleration in a four pulley system?

The relationship between double differentiation and acceleration in a four pulley system is that double differentiation is used to calculate the acceleration of the system. By taking the second derivative of the velocity or displacement function, we can determine the acceleration of the system at any given time.