# Chain of mass M with length L (SPhO 2009)

• mesmeriz3
These include neglecting air resistance and assuming that the chain falls straight down without any swinging or twisting.In summary, a chain of mass M and length L is released and falls onto a scale, with its lower end touching the scale. The reading of the scale when a length of the chain x has fallen can be found by neglecting the size of individual links and applying the equation F = dp/dt. Several assumptions must be made to simplify the problem, such as neglecting air resistance and assuming a straight downward fall without swinging or twisting.
mesmeriz3

## Homework Statement

A chain of mass M and length L is suspended vertically with its lower end touching a
scale. The chain is released and falls onto the scale. What is the reading of the scale
when a length of the chain x has fallen? You may neglect the size of the individual

-

## The Attempt at a Solution

Initial W(on scale)= Mg
Final W= mx/L

Classical one.
Notice that the chain has linear momentum. By applying F = dp/dt, you will see the result is not mx/L
There are several assumptions to be made in order to simplify the problem.

## 1. What is the equation for the potential energy of a chain of mass M with length L?

The equation for the potential energy of a chain is given by U = MgL, where M is the mass of the chain, g is the acceleration due to gravity, and L is the length of the chain.

## 2. How does the potential energy of the chain change as its length increases?

As the length of the chain increases, the potential energy also increases. This is because the gravitational force acting on the chain increases as the length increases, resulting in a higher potential energy.

## 3. What is the significance of the mass of the chain in this scenario?

The mass of the chain plays a role in determining the potential energy of the chain. A heavier chain will have a higher potential energy compared to a lighter chain with the same length, as the gravitational force acting on it will be greater.

## 4. How does the potential energy of the chain change if it is held at different angles?

The potential energy of the chain is dependent on the height at which it is held. If the chain is held at a higher angle, the potential energy will be higher compared to when it is held at a lower angle.

## 5. What are some real-life applications of this concept?

The concept of potential energy in a chain has practical applications in engineering and construction, such as in the design of suspension bridges and elevators. It is also relevant in physics experiments and simulations to study the behavior of complex systems under the influence of gravity.

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