# length of a simple pendulum affects the time

. Plan

Aim

To investigate how the length of a simple pendulum affects the time for a complete swing.

Variables

length

The length of the pendulum has a large effect on the time for a complete swing. As the pendulum gets longer the time increases.

size of swing

Surprisingly, the size of the swing does not have much effect on the time per swing.

mass

The mass of the pendulum also does not affect the time.

air resistance

With a small pendulum bob there is very little air resistance. This can easily be seen because it takes a long time for the pendulum to stop swinging, so only a small amount of energy is lost on each swing. A large and light pendulum bob would be affected by a significant amount of air resistance. This might change the way the pendulum moves.

gravity

The pendulum is moved by the force of gravity pulling on it. On the Moon, where the pull of gravity is less, I would expect the time for each swing to be longer.

Theory

When the pendulum is at the top of its swing it is momentarily stationary. It has zero kinetic energy and maximum gravitational potential energy. As the pendulum falls the potential energy is transferred to kinetic energy. The speed increases as the pendulum falls and reaches a maximum at the bottom of the swing. Here the speed and kinetic energy are a maximum, and the potential energy is a minimum. As the pendulum rises the kinetic energy is transferred back to potential energy. The speed of the pendulum decreases and falls to zero as it reaches the top of its swing, with the potential energy a maximum again.

A small amount of energy is lost due to air resistance as the pendulum swings. This means each swing is slightly smaller than the one before.

There are two forces acting on the pendulum bob. Gravity tries to pull the bob downwards but this is resisted by the tension in the string. As there are only two forces they can only be balanced when they are in opposite directions. This only occurs when the pendulum is in the middle of its swing, so for the rest of the time the two forces are unbalanced; hence the bob swings back and forth.

The two forces are equal and opposite.
This means there is no resultant force on the bob.
It could either be stationary, or passing through the middle of the swing.

force due to gravity = weight of bob = mg

m = mass of bob
g = gravitational field strength
g = 10 N/kg at the Earth's surface

The two forces are not in opposite directions. This means there is a resultant force on the bob to the right.

If the bob is moving to the right the force makes it accelerate and the speed increases as it moves towards the centre.
If the bob is moving to the left the force decelerates it and it slows down.

Prediction

The diagram shows the arcs through which two pendulums swing. The red one is twice the length of the blue one. Notice that the blue arc is always at a steeper angle than the red arc, ...

#### Here's what a star student thought of this essay

His table is clear and plotting his average results on a graph, his results are clearly shown. He plots his independent variable on the y axis and depenent on the x axis as you are meant to. There are very few spelling or grammatical errors.

The student shows his method well and tries to reduce errors by thinking of how to do his experiment while reducing errors. Which I would recommend always doing as it is best to know what you are doing before you do it, you don't want to be confused as to what to do when you get to the experiment. He takes an appropriate number of repeats making his experiment more reliable. He makes sure to control all variables other than his dependent and independent variables as meant. You must be careful to do this as if you don't you could get incorrect results.

The student answers the question well, he at first explains the theory then makes predictions based on theory. I would recommend this as you get your marks for explaining why something will happen, not just stating it will. This student explains why using theory very well. He makes a table which shows that as length increases so does the time period, and a graph. He also goes further and plots a graph of the time period against the square root of length, to prove that the theory is correct and that T is proportional to the square root of length.