Understanding Simple Pendulum Experiment: Water-Filled Sphere Explanation

[bc64846]

This is my first time ever taking a physics class...and needed an explanation. In lab we're doing a simple pendulum experiment. Given the equation T=2pi(sqrt L/g) and noting observations with different pendulum lengths we must then answer this question:

A hollow sphere is filled with water and suspended by a long thread. A small hole is made in the bottom of the sphere and as the water flows out one observes that the period of oscillation of the simple pendulum first increases and then decreases. Explain.

 

[mgb_phys]

The 'L' in the above equation is the length from the fixed end to the centre of gravity of the string+bob (the weight on the end of the string).
Where is the centre of gravity if the bob is much heavier than the string and where if the bob and the string have the same weight?

Slightly nasty question - the simple equation above normally assumes that all the weight is in the bob, there is a more complex equation if you need to take into account different weights.

 

[charng]

First of all, congratulations on taking your first physics class! The simple pendulum experiment is a great way to start learning about the principles of physics.

Now, let's break down the explanation for the observations in the experiment. The equation T=2pi(sqrt L/g) represents the relationship between the period of oscillation (T), the length of the pendulum (L), and the acceleration due to gravity (g). This equation tells us that the period of oscillation is directly proportional to the square root of the length of the pendulum and inversely proportional to the acceleration due to gravity.

In the experiment, a hollow sphere is filled with water and suspended by a long thread. When a small hole is made in the bottom of the sphere, the water starts to flow out. As the water flows out, the mass of the sphere decreases. This means that the acceleration due to gravity also decreases because gravity is pulling on a smaller mass.

According to the equation, as the acceleration due to gravity decreases, the period of oscillation should increase. This is because the pendulum is now experiencing a weaker force of gravity, so it takes longer for it to complete one full oscillation.

However, as more water flows out of the sphere, the mass of the sphere decreases even further. This means that the acceleration due to gravity continues to decrease. At a certain point, the period of oscillation reaches its maximum value.

But as the water continues to flow out and the mass of the sphere decreases even more, the acceleration due to gravity starts to increase again. This is because now the pendulum is experiencing a stronger force of gravity as it is being pulled towards the center of the Earth by a smaller mass.

As a result, the period of oscillation starts to decrease again until all the water has flowed out of the sphere and the mass of the sphere is at its lowest value. At this point, the acceleration due to gravity is at its highest value, and the period of oscillation is at its lowest value.

In summary, the observations in the experiment can be explained by the fact that the period of oscillation is affected by both the length of the pendulum and the acceleration due to gravity, and as the mass of the sphere changes due to the water flowing out, the acceleration due to gravity also changes, resulting in changes in the period of oscillation. I hope this helps to clarify the concept of simple pendulum and the relationship between its period and the variables involved.