PHYS 1401 Lab-06: Simple Pendulum Essay

PHYS 1401 Lab-06: Simple Pendulum Essay

Instructions/Descriptions

PHYS 1401 Lab-06: Simple Pendulum Essay

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Objectives

• Investigate the factors affecting time period of a simple pendulum.
• Investigate the motion of a simple pendulum to determine the acceleration due to gravity.
• To understand the relationships of the energetics, forces, acceleration, and velocity of an oscillating pendulum.

Simple Pendulum

A simple pendulum is defined, ideally, as a particle suspended by a weightless string. Practically, it consists of a small body, usually a sphere, suspended by a string whose mass is negligible in comparison with that of the sphere, and whose length is very much greater than the radius of the sphere.

Under these conditions, the mass of the system may be considered as concentrated at a point, namely the center of the sphere and the problem may be handled by considering the motion of the suspended body, commonly called the “bob”, along a circular arc.

We will use the PhET simulation Pendulum Lab. This simulation mimics a real pendulum and allows you to adjust the initial position, the mass, and the length of the pendulum.

1. Open PhET Simulation https://phet.colorado.edu/sims/html/pendulum-lab/latest/pendulum-lab_en.html

You can drag the pendulum to an arbitrary initial angle and release it from rest. You can adjust the length and the mass of the pendulum using the slider bars at the top of the panel. Velocity and acceleration vectors can be selected to be shown, as well as the forms of energy.

Feel free to play around with the simulation. When you are done, click the Reset button.

Activity 1: Energy of Simple Pendulum

2. Select to show the energy of pendulum 1. Be sure that friction is set to none. Drag the pendulum to an angle (with respect to the vertical) of 30, and then release it.

Question-1: When the pendulum is at −30, what form(s) of energy does it have?

1. a) Potential Energy
2. b) Kinetic Energy
3. c) Thermal Energy
4. Drag the pendulum to an angle (with respect to the vertical) of -30 and then release it.

Question-2: Where is the pendulum swinging the fastest?

1. a) At -30
2. b) At 0
3. c) At 15
4. d) At 30
5. Drag the pendulum to an angle (with respect to the vertical) of 30, and then release it. Select to show the acceleration vector.

Question-3: With the pendulum swinging back and forth, at which locations is the acceleration equal to zero?

30. a) The acceleration is zero when the angle is either +30 or −30.
31. b) The acceleration is never equal to zero as it swings back and forth.
32. c) The acceleration is zero when the angle is 0

Question-4: With the pendulum swinging back and forth, how does the tension of the rope compare to the force of gravity when the angle is 0?

1. a) The tension is greater than the force of gravity.
2. b) The tension is greater than the force of gravity only if it is swinging really fast.
3. c) The tension is less than the force of gravity.
4. d) The tension is equal to the force of gravity.

You will investigate how the period of oscillation depends on the properties of the pendulum. The period of oscillation is the amount of time it takes for the pendulum to take a full swing, going from the original angle to the other side, and returning to the original angle.

Frequency is defined as the number of oscillations occurring in one second.

Activity 2: Time Period vs Length of Pendulum

1) Set the gravity to Earth (9.81 m/s2), friction to 0, and the mass of the object to 1 kg.

2) Set the length of pendulum to 0.3 m

3) Drag the object to 20° and release.

4) Click the period timer button in the bottom left corner. Click on the play button and record the period in Table-1.

Table-1

Question-5: How does the period of the pendulum vary with the length of the pendulum?

Activity 3: Time Period vs Mass of Pendulum

1. Set the gravity to Earth (9.81 m/s2), friction to 0, and the length of pendulum to 1.0 m.
2. Set the mass of the object to 0.5 kg.
3. Drag the object to 20° and release.
4. Click the period timer button in the bottom left corner. Click on the play button and record the period in the data table, Table-2.
5. Repeat the steps 2 – 4 two more times by increasing the mass by 0.5 kg each time.

Table-2

Question-6: How does the period of the pendulum vary with the mass of the pendulum?

Set up two pendulums by selecting Show 2nd pendulum. Adjust the lengths to be the same and have one pendulum with a higher mass. You can release one and then release the other, with the same angle, when the first one is back at that angle.

Question-7: How does the period of the pendulum depend on mass?

1. a) A heavier pendulum has a longer period.
2. b) A heavier pendulum has a shorter period.
3. c) The period is independent of the pendulum’s mass.

Activity 4: Time Period vs Initial Angle of Pendulum

1. Set the gravity to Earth (9.81 m/s2), friction to 0, the length of pendulum to 1.0 m, and the mass of the object to 1.0 kg.
2. Click Reset, and then drag the pendulum to an angle (with respect to the vertical) of 10 and release it. Click the period timer button in the bottom left corner. Click on the play button and record the period in the data table, Table-3.

Table-3

Question-8: How does the period of oscillation depend on the initial angle of the pendulum when released?

1. a) The period is independent of the initial angle.
2. b) The period is longer when the initial angle is greater.
3. c) The period is shorter when the initial angle is greater.

For small angles (e.g., <30), it is a pretty good approximation that the period doesn’t change, but for larger angles the period does in fact increase.

Question-9: Suppose the initial angle was increased to 90°, how does this change affect the period of the pendulum?

Activity 5: Time Period vs gravity

1. Set the friction to 0, the length of pendulum to 1.0 m, and the mass of the object to 1.0 kg.
2. Set the gravity to Earth (9.81 m/s2).
3. Drag the object to 20° and release.
4. Click the period timer button in the bottom left corner. Click on the play button and record the period in the data table.
5. Repeat the steps 2 – 4 two more times by changing the gravity and record the values in

Table-4.

Table-4

Question-10: How does the period of oscillation depend on the value of g?

1. a) The period of oscillation is longer on planets with a higher value of g.
2. b) The period of oscillation is shorter on planets with a higher value of g.
3. c) The period of oscillation is independent of the value of g.

In fact, for small angles of oscillation the period T for a pendulum is nearly independent of amplitude, especially if θ is less than about 15°. The period T is inversely proportional to the square root of g;

where L is the length of the pendulum and T is the period.

The time period for a pendulum is given by the theoretical formula:

Question-11: Using the length of pendulum L =1.0 m, and the mass m =1.0 kg, calculate the acceleration due to gravity on Planet X. Show your work.

Question-12: How will friction affect the time period of the pendulum?

Conclusion: Summarize, in few sentences, the factors which affect the time period of the pendulum.

PHYS 1401 Lab-06: Simple Pendulum Essay

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