# Displacement of centre of mass

• utkarshakash
In summary, the conversation discusses a problem involving a pulley system with a man and a counterweight connected by a rope. The task is to find the displacement of the center of mass of the system when the man climbs a distance h. The solution involves considering the equilibrium of the system and taking into account the mass of the ladder. The correct answer is mh/2M.
utkarshakash
Gold Member

## Homework Statement

A pulley fixed to a rigid support carries a rope whose one end is tied to a ladder with a man and the other end to a counterweight of mass M. The man of mass m climbs up a distance h with respect to the ladder and then stops. If the mass of the rope and the friction in the pulley axle are negligible, find the displacement of the centre of mass of this system.

## Homework Equations

COM$_{y}$=my$_{1}$+my$_{2}$/m+M

## The Attempt at a Solution

Let the y-coordinate of man be l and that of mass M be 0. Since it goes up a height h
∴ y-coordinate of the man changes to (l+h) but that of mass M remains unchanged.
So, if I subtract the final COM from initial COM I get the answer mh/m+M. But the correct answer is mh/2M. I'm unable to bring out mistake in my solution.

Before man starts climbing the ladder, whether the system is in equilibrium? If yes, you have to take into account the mass of the ladder, which is M- m.

Oh, I forgot that the system is in equilibrium. I must have noticed the word counterweight. This is the key to the answer. Thanks so much as now I have arrived at the correct answer.

## 1. What is the definition of displacement of centre of mass?

The displacement of centre of mass is the measurement of the change in position of the centre of mass of an object from its initial position to its final position. It is a vector quantity and is typically measured in units of meters (m).

## 2. How is displacement of centre of mass calculated?

The displacement of centre of mass can be calculated by taking the difference between the final and initial positions of the centre of mass. This can be represented by the formula: Δx = xf - xi, where Δx is the displacement, xf is the final position, and xi is the initial position.

## 3. What factors can affect the displacement of centre of mass?

The displacement of centre of mass can be affected by various factors such as the shape, size, and mass distribution of the object, as well as external forces acting on the object. The displacement can also be affected by changes in the position of the object's individual components.

## 4. How is displacement of centre of mass related to stability?

The displacement of centre of mass is directly related to the stability of an object. A lower displacement of centre of mass means the object is more stable, while a higher displacement means the object is less stable. This is because a lower displacement indicates that the centre of mass is closer to the base of the object, providing a more stable foundation.

## 5. Why is it important to understand displacement of centre of mass?

Understanding displacement of centre of mass is important in many fields such as physics, engineering, and sports. It helps in analyzing the stability of structures and designing structures that can withstand external forces. In sports, understanding the displacement of centre of mass can help athletes improve their balance, stability, and performance.

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