For my practical coursework I have to find out how mass, amplitude or the length of the string affect the period of a pendulum. I have decided to find out how mass affects the period.

Diagram

Method

1. Set-up the equipment as in the diagram above.

2. Swing the pendulum with 100g weight on the end from an amplitude of 20cm and record how long it takes for the pendulum to got through 20 cycles and divide it by 20.

3. Repeat 2 more times with 100g.

4. Repeat steps 2 and 3 with 200g, then 300g, then 400g and then 500g and record the results.

Fair testing

1. I must keep the length of the string at 50cm

2. I must make sure I drop the pendulum from amplitude of 20cm.

3. I must not push the pendulum.

Prediction

I predict that for every different weight the period will stay roughly the same. I predict this because when working out velocity you use this formula:

V= ?2 x kinetic energy

Mass

Potential energy can e substituted for kinetic energy, as the kinetic energy when the string is perpendicular to the earth is equal to the potential energy when the weight is 20cm above this point. So the formula can be:

V= ?2 x potential energy

Mass

Potential energy =mass x gravitational pull x amplitude. So if this is substituted in the formula looks like this:

V= ?2 x mgh

M

The mass on top and below cancels each other out. This means it cannot affect the period. This is because gravity adapts itself according to the mass of an object i.e. a 1 kilo weight has 9.8 N/kg of gravitational pull. Whereas a 100 kilo weight has 980 N/kg of gravitational pull. This means the velocity of two equal sized objects weighing 1 kilo and 100kilos is equal.

My prediction could be wrong because the surface area increases as I add more weight. A bigger surface area has more air resistance, which will slow down the pendulum. However the effect will be small.

Although I think that mass does not change it I do however think that the length of the string will because:

Period = 2 X ? X ?length of string

Gravitational pull (9.8)

This means if you change the length of the string this affects the answer to the equation – if the string is longer the answer (time) is longer and vice versa.

Results

100g

200g

300g

400g

500g

Attempt 1 (20)

33.11

33.48

33.39

33.34

33.31

Attempt 1 (1)

1.6555

1.674

1.6695

1.667

1.6655

Attempt 2 (20)

33.24

33.45

33.22

33.30

33.22

Attempt 2 (1)

1.662

1.6725

1.661

1.665

1.661

Attempt 3 (20)

33.28

33.42

33.14

33.41

33.24

Attempt 3 (1)

1.660

1.671

1.657

1.6705

1.662

Average

1.660

1.6725

1.6625

1.6675

1.662

Conclusion

I conclude that my prediction was correct. I found out that when you change the mass of a pendulum it does not affect the period. The period did vary slightly but not due to the mass. I believe that what I explained in my prediction was correct and that that is the reason for my results.

Evaluation

I think that the experiment went well, however if I were to do it again I would allow myself more time so that I could see if my prediction about the length of the string was correct. Also I would use lighter weights, as the heavier weights were very hard to get 20 swings out of without hitting the table.