Name: Airen Nickerberry Pendulum

Go to http://phet.colorado.edu/simulations/sims.php?sim=Pendulum_Lab

and click on Run Now.

1. Research to find equations that would help you find g using a pendulum. Design an experiment and test your design using Moon and Jupiter. Write your procedure in a paragraph that another student could use to verify your results. Show your data, graphs, and calculations that support your strategy.

The time it takes a pendulum to complete one back-and-forth swing, called the pendulum’s period, depends only on the pendulum’s length and the value of gravity. In an experiment, an experimenter can easily manipulate a pendulum’s length. The value of gravity cannot be manipulated. A simple pendulum consists of a particle of mass m, attached to a frictionless pivot by a cable of length L and negligible mass. When the particle is pulled away from its equilibrium position by an angle and released, it swings back and forth. The period of an simple pendulum can be found

with the formula: The equation for g written in terms of period T is where g is gravity, L is the length of the pendulum, and T is the period of the pendulum:

In order to find g of a pendulum for the Moon and Earth, you would first need to go to http://phet.colorado.edu/simulations/sims.php?sim=Pendulum_Lab. Click Run and keep the settings the same. (Mass=1kg, Length 2m, No friction, Real Time).

We will begin with the Moon. Do at least 10 trials with varying lengths, but always starting the pendulum at fifteen degrees. Record the Length (L) of the pendulum, the time to complete a period (T) in seconds, and T^2 (just to make it easier to plug into the equation later) for each trial.Either take the average of the gravities found after plugging in L and T^2 or you can plot a line of best fit to determine the gravity of a planet/moon and get rid of any outliers.

Moon:Trial Length of the

Pendulum (L)Time to

complete period (T)

T^2 Gravity (g)

1 2.00 m 6.91 s 47.7 1.66 m/sec22 1.40 m 5.78 s 33.4 1.65 m/sec23 1.25 m 5.46 s 29.8 1.66 m/sec24 1.92 m 6.77 s 45.8 1.66 m/sec25 1.83 m 6.61 s 43.7 1.65 m/sec26 1.14 m 5.23 s 27.4 1.64 m/sec2

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7 0.83 m 4.45 s 19.8 1.66 m/sec28 1.67 m 6.31 s 39.8 1.66 m/sec29 1.32 m 5.61 s 31.5 1.65 m/sec210 1.58 m 6.14 s 37.7 1.65 m/sec2

Average g=1.654Earth:

Trial Length of the Pendulum (L)

Time to complete period (T)

T^2 Gravity (g)

1 2.00 m 2.85 s 8.12 9.72 m/sec22 1.40 m 2.38 s 5.66 9.77 m/sec23 1.25 m 2.25 s 5.06 9.75 m/sec24 1.92 m 2.79 s 7.78 9.74 m/sec25 1.83 m 2.73 s 7.45 9.70 m/sec26 1.14 m 2.15 s 4.62 9.74 m/sec27 0.83 m 1.84 s 3.39 9.67 m/sec28 1.67 m 2.60 s 6.76 9.75 m/sec29 1.32 m 2.32 s 5.38 9.69 m/sec210 1.58 m 2.53 s 6.40 9.75 m/sec2

Average g=9.728

2. Use your procedure to find g on Planet X. Show your data, graphs, and calculations that support your conclusion.

Planet X:Trial Length of the

Pendulum (L)Time to

complete period (T)

T^2 Gravity (g)

1 2.00 m 2.37 s 5.62 14.1 m/sec22 1.40 m 1.98 s 3.92 14.1 m/sec23 1.25 m 1.87 s 3.50 14.1 m/sec24 1.92 m 2.32 s 5.38 14.1 m/sec25 1.83 m 2.27 s 5.15 14.0 m/sec26 1.14 m 1.79 s 3.20 14.1 m/sec27 0.83 m 1.53 s 2.34 14.0 m/sec28 1.67 m 2.16 s 4.67 14.1 m/sec29 1.32 m 1.92 s 3.69 14.1 m/sec210 1.58 m 2.11 s 4.45 14.0 m/sec2

Average g=14.07

3. Give your conclusion and write an error analysis. I conclude that due to the methods utilized to ascertain the g of the moon (1.65) and

earth (9.73), the g of Planet X would have to be 14.1. There are a few areas that could have caused errors in the math. The rounding of the decimals could be less

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than exact. There could also be a lack of diversity in the length of the pendulum numbers and the number of trials. However, the whole numbers of each g average should be fairly accurate.

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