Question

Determination of g_planet from the Period data of the Pendulum Virtual Lab

Learning Objective: Use the dimensions and period of a pendulum to determine the gravitational acceleration of the planet on which the pendulum is set in motion.

Go to the University of Colorado – Boulder PhET website/Pendulum Lab. Conduct four experiments with a 1 kg mass and a 10° pull-back angle from the vertical as controlled variables. The pendulum lengths should be between 0.250 m to 2.500 m, inclusive. Using the photogate timer, determine the period of the pendulum, in seconds.

The studied planet is ______Earth_______. Theoretical value of g for the planet_____9.81m/s^2______

Table 1. Relationship between the Length, l (m), and the Period of the Pendulum, T, (s).

	Experiment #1	Experiment #2	Experiment #3	Experiment #4
String Length (m)	0.70m	0.71m	0.72m	0.73m
Period, T (s)	1.6813s	1.6945s	1.7063s	1.7181s

1. Using the data in Table 1, find the product between the string length and 4π² and record it in the first row of Table 2, below.
2. Calculate the square of the periods on Table 1 in the second row of Table 2, below.

Table 2. Relationship between the String Length, l (m), and the Square of the Period of One Oscillation of a Pendulum, T², (s²).

	Experiment #1	Experiment #2	Experiment #3	Experiment #4
String Length times 4π2 (m)	27.63m	28.02m	28.42m	28.81m
Square of the Period (s2)	2.8267s^2	2.8713s^2	2.9114s^2	2.9518s^2

3. At small angles, θ, the Period of a Pendulum, T, and the length of the string, l, are related by the formula:

T² = 4π²l/g,           where g is the acceleration by gravity.

Rearranging the equation, 4π²l = g T²

4. With your graphing calculator, enter T² as L₁ and 4π²l as L₂. Build a graph with L₁ as the abscissa (x-axis), and L₂ as the ordinate (y-axis). Otherwise, use an Excel spreadsheet to prepare your data table and make a graph. Do a linear regression. The average value of g is the slope of the line, in m/s².

5. What is the experimental average value of the determined g for the planet ________________?

6. Compare your experimental and theoretical values.

7. Repeat the experiment for planet X and determine the value of g for planet X___________

Please work out and explain in detail for #4 and #5.

Answer 1

Here in this experiment of determining the experimental value of acceleration due to gravity of the planet earth from the experiment of measuring the varying values of the time period of the simple pendulum on the corresponding variations in the length of the string of the pendulum in each trials ,with the readings of the length is in between taken in between 0.25 to 2.5m for the mass of 1 kg of the bob is hanged in the penduum.

it is conducted the 4 experiments to take the reading of the time period of the pendulum for the variable lengths as given,(table 1)

	Experiment 1	Experiment 2	Experiment 3	Experiment 4
string length(m)	0.70m	0.71m	0.72m	0.73m
Period T(s)	1.6813s	1.6945s	1.7063s	1.7181s

As we already know that,time period of the pendulum for the length of the string,

Ie,

Here on squaring both sides of eqn,

Fro this we have acceleration due to gravity,

So,it shows that the value of is the ratio of and the time period of pendulum()

Or the graph plotted with along x axis and on Y axis will be the straight line with a slope equals to the acceleration due to gravity( ).

So,for plotting graph,fromulated the Table 2 for and from table 1,As given in qn,

	Experiment 1	Experiment 2	Experiment 3	Experiment 4
	27.63m	28.02m	28.42m	28.81m
	2.8267	2.8713	2.9114	2.9518

Then plotting the graph (on x axis) v/s (on y axis) in excel

Here from the graph the line of equation of the trendline of the plotted graph as shown is given as,

it is in the form of

So slope of trendline of the graph ,

So,the slope of graph,Experimental value of g,=

We have given that the theoretical value of g as,

Here the above values shows that the theoretical value of acceleration due to gravity is greater than the value of acceleration due to gravity.

So,the percentage difference experimental value of g to theoretical value,

%

Please upvote the answer...