## Introduction

In this article, you will learn how to find the length of a wire that is 10 meters long and holds a weight on its end with a pendulum. You will also learn how to calculate the temperature increase at the weight’s end when it is 20 degrees Celsius.

## Let’s solve our problem

When we increase the temperature of an object, it will contract (shrink) in size. For example, if we put a metal wire into hot water, the wire will shrink in size.

Similarly, when we decrease the temperature of an object, it will expand (grow) in size. For example, if we put a metal wire into cold water, the wire will expand in size.

We need to know how much the object will shrink and grow when its temperature increases or decreases by °C. To do this problem, we need to use the mathematical formula known as an equation of state.

## Solving for X

To solve for X, we first need to find out what temperature increase causes the alambre de acero to stretch. To do this, we use the following equation:

ext{Alambre de acero} = \dfrac{1}{k}\left( {X – {T_0}} \right)

Where:

ext{Alambre de acero} = The alambre of steel in question

\dfrac{1}{k} = Steel’s Young’s modulus (a measure of its strength)

\left( {X- {T_0}} \right) = The temperature increase that causes the alambre of steel to stretch

## Applying the Law of Total Momentum

When we consider a weight held at one end of an extended cable, the net force on the weight is zero because the cable has been extended infinitely. The net force on the weight is also zero if the weight is balanced on both ends of the cable. In both cases, there is no moment of inertia (I) about any center.

If we increase the temperature of the weight, then its momentum will also increase. This means that the total net force on the weight will also increase. In fact, according to Newton’s second law of motion (Fnet = Ia), for a constant mass and velocity, the total net force always increases as temperature increases. This is shown in Figure 1-1.

## Finding the Maximum Length of the Cord

When it comes to temperature, metal has a limited range. Depending on the metal, it can go from very cold to very hot.

When we measure the length of a metal cord, we’re really measuring how much heat it can take before it breaks. We call this the maximum tempering (or working) temperature.

Think about it this way: If you have a piece of metal that is really cold, it will take a lot of heat to make it hot enough so that you can work with it. Likewise, if the metal is really hot, it will take very little heat to make it workable.

In the case of a metal cord, the maximum tempering temperature is determined by its thickness and its alloy. Thicker metals will have a higher maximum tempering temperature than thin metals. And different alloys will have different maximum tempering temperatures.

For example, an alambre de acero (steel wire) has a maximum tempering temperature of 850°C (1,740°F). This means that if you want to use steel wire as a cord, make sure that the cord you choose has a thickness that is at or below 850°C (1,740°

## Calculating the Temperature Change

To calculate the length of the wire that supports a pendulum at different temperatures, first you need to know the temperature change in degrees Celsius. This is done by dividing the temperature at the beginning of the experiment by the temperature at the end. Then, you multiply this number by 100 to get mm. (For example, if the temperature at the beginning and end of the experiment was 20°C and 30°C respectively, then the temperature change would be 200°C/30°C = 6.67mm).

The farther away from equilibrium the pendulum is, the greater the temperature change will be. This is because there is more energy available to do work (move atoms around) as temperatures change. So, a long wire will support a heavier pendulum at a greater temperature change than a short wire will.

## Conclusion

Un alambre de acero de 10.00m sostiene una lenteja de péndulo en su extremo¿Cuánto milímetros se alarga cuando su temperatura aumenta 20,0°C? La respuesta es que el alambre se encogerá porque la fuerza túnelsea tendrá más presión sobre él y estarán separadas las moléculas del hilo conductor, lo cual hará que el material se contraiga.

## FAQ

How long does a metal wire support a pendulum’s weight if it warms up by 3°C?

Assuming the metal wire has the same diameter at both ends and is made of the same material, the wire will support twice as much weight when it warms up by 3°C. Therefore, the pendulum will be supported by the wire for 6.25 cm when it is heated up by 3°C.

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