• Author / Uploaded
• Martine Gjermundsen Ræstad

Citation preview

Physics report – Simple pendulum

1.j 2013/14

Hanne Martine G. Ræstad

Simple Pendulum Investigation of gravity and restoring force

Aim To determine acceleration due to gravity by measuring the time period of a simple pendulum.

Theory A simple pendulum is a weight suspended by a string or rod so that it is allowed to swing freely. When the weight is swinging back and forth with a steady, uninterrupted rhythm, it is oscillating. The path from the equilibrium position (see diagram) to the point B, to the point A, and back to the equilibrium positing is called an oscillation. In a pendulum motion, the energy of the bob is transferred between potential and kinetic energy. At the points A and B the bob has the most potential energy and no kinetic energy, but the energy is then steadily transferred to kinetic energy until the bob reaches the equilibrium position where it has the most kinetic energy and no potential energy. The force which pulls the bob back towards the equilibrium position is called the restoring force. In a pendulum motion, the restoring force is directly proportional to the displacement of the object directed opposite to the restoring force – as shown in the formula: F – restoring force y - displacement

Therefore the motion of a simple pendulum is called a simple harmonic motion. The experiment was conducted by varying lengths (L) of the pendulum. A pendulum executes periodic motion. A periodic motion is that which repeats after regular intervals of time. Hence, the time period of a simple pendulum is determined by the formula: L – Length of pendulum g – acceleration due to gravity T – time period

√

Apparatus Inextensible string

Steel weight

Ruler (1 m)

Stand

Stopwatch (mobile phone)

Clamp

Procedure First, we assembled the simple pendulum. For this we used the clamp, the stand, the string and the steel weight. The clamp was attached to the stand, which was placed on the edge of a table with the

Side 1 av 4

Physics report – Simple pendulum

1.j 2013/14

Hanne Martine G. Ræstad

clamp facing outwards. The string was tied to the steel weight on one end, while the other end was led through the clamp and tied to the stand. The length of the string from the point of suspension to the middle of the steel weight was measured with a ruler. We began with the length of 90 cm. The pendulum was raised so that the string would be at an approximate 45-degree angle from the equilibrium position, then dropped. The time was measured from the moment when the pendulum had completed one oscillation, and then 20 oscillations were measured. This was repeated three times. The reason for both the number of tries and the number of oscillations measured is accuracy. Measuring 20 oscillations and dividing by 20 will give a more precise result than measuring 1 oscillation alone would. In the same way, taking the average of three attempts will give a more precise result than only taking the result of one attempt. The experiment was repeated seven times, using different lengths for the pendulum. The pendulum was made shorter every time, so as to make it easier for us to get an accurate length using our method of tying the string to the stand.

Data Raw data Length of pendulum (L) [m] 0.60 0.65 0.70 0.75 0.80 0.85 0.90

Time for 20 oscillations (t1) [s] 31.60 32.88 34.05 35.19 36.53 37.63 38.81

Time for 20 oscillations (t2) [s] 31.67 32.77 34.29 35.18 36.35 37.20 39.62

Time for 20 oscillations (t3) [s] 31.66 32.89 34.40 35.23 36.26 37.19 41.35

Processed data Length of pendulum (L) [cm]

Mean/Average time for 20 oscillations ( ) [s]

Time for 1 oscillation (T) { } [s]

Time for 1 oscillation squared (T2) [s2]

60 65 70 75 80 85 90

31.64 32.85 34.25 35.20 36.39 37.34 39.93

1.58 1.64 1.71 1.76 1.82 1.87 2

2.5 2.69 2.92 3.1 3.31 3.5 4

Looking back on our formula for T √

Side 2 av 4

L – Length of pendulum g – acceleration due to gravity T – time period

Physics report – Simple pendulum

1.j 2013/14

Hanne Martine G. Ræstad

We can rearrange it to isolate g, as finding g is the aim of this experiment.

Temporarily looking away from the constant value of

, we are left with the fraction

.

We can plot a graph using the information attained in the experiment. As L is the independent variable, we will place the L-values on the x-axis. T2 is then the dependent variable and will be placed on the y-axis.

The slope of the graph will then be

, and to get

we will take the inverse of the slope. As the slope

of the graph is 4.65, the inverse will be

(= 0.215).

We can then reintroduce the constant

to the equation, which will now look like this

Calculating that, the result will be

Conclusion The value calculated for acceleration due to gravity in our experiment is 8.488 m/s2. The standard value for acceleration due to gravity is 9.806 m/s2.

Percentage error We use this formula to calculate the percentage error of our experiment: Side 3 av 4

Physics report – Simple pendulum

Inserting the values, this will give

1.j 2013/14

Hanne Martine G. Ræstad

= 13.4%

There are many factors which could have influenced our results. First of all, the length of the string might have varied slightly, either because of inaccurate measurement or any stretch which might have lengthened the string. The angle which the pendulum was dropped from might also have varied slightly, and the pendulum did most likely not swing in perfect simple harmonic motion the entire time. The time is also likely to not have been measured perfectly, as it is very difficult to start and stop the timer at precisely the right moment. A negligible difference might have been caused by rounding off numbers to fewer decimals in the data and calculations, and friction and air resistance slowing the pendulum down.

Side 4 av 4