Online-LAB-06_Simple-Pendulum

PHYS 1401 Lab-06: Simple Pendulum Name: _shahd Mohamed kheir_______________________ 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 b) Kinetic Energy c) Thermal Energy ANSWER; Potential energy The pendulum starts off with no kinetic energy since it is released from rest, so it initially only has potential energy. When the pendulum is at−30 ∘ , it is just as high above the ground as when it started, so it must have the same amount of potential energy as it initially had. 3. 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? a) At -30  b) At 0  c) At 15  d) At 30  ANSWER; at 0 ∘ The pendulum has the least potential energy at this location since it is at the lowest point in the arc (in fact, for this simulation, the potential energy reference location is here, so it has no potential energy). This means that the kinetic energy is greatest here, so the pendulum is moving the fastest. 4. 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? a) The acceleration is zero when the angle is either +30  or −30  . b) The acceleration is never equal to zero as it swings back and forth. c) The acceleration is zero when the angle is 0  The acceleration is never equal to zero as it swings back and forth. The pendulum is moving in a circular path so its velocity is never constant. 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  ? a) The tension is greater than the force of gravity. b) The tension is greater than the force of gravity only if it is swinging really fast. c) The tension is less than the force of gravity. d) The tension is equal to the force of gravity. 2

Question-5: How does the period of the pendulum vary with the length of the pendulum? The period of a pendulum does not depend on the mass of the ball, but only on the length of the string. Two pendula with different masses but the same length will have the same period. Two pendulums with different lengths will have different periods; the pendulum with the longer string will have the longer period. Activity 3: Time Period vs Mass of Pendulum 1. Set the gravity to Earth (9.81 m/s 2 ), 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 Length of Pendulum (in m) Mass of Pendulum (in kg) Period (in s) 1.0 0.5 2.0215s 1.0 1.0 2.0125s 1.0 1.5 2.0125s Question-6: How does the period of the pendulum vary with the mass of the pendulum? The period of a pendulum does not depend on the mass of the pendulum. The period of a simple pendulum (a weight attached to a string or rod) is determined only by its length and the acceleration due to gravity. The mass of the pendulum bob does not affect the time it takes for the pendulum to complete one full swing back and forth. 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? a) A heavier pendulum has a longer period. b) A heavier pendulum has a shorter period. c) The period is independent of the pendulum’s mass. ANSWER; The period is independent of the pendulum's mass. 4

Activity 4: Time Period vs Initial Angle of Pendulum 1. Set the gravity to Earth (9.81 m/s 2 ), 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 Length of Pendulum (in m) Initial angle (in degrees) Period (in s) 1.0 5° 2.0070s 1.0 10° 2.0099s 1.0 30° 2.0410s 1.0 45° 2.0863s 1.0 60° 2.1529s Question-8: How does the period of oscillation depend on the initial angle of the pendulum when released? a) The period is independent of the initial angle. b) The period is longer when the initial angle is greater. c) The period is shorter when the initial angle is greater. The period is longer when the initial angle is greater. Unlike a harmonic oscillator such as a mass on a spring, the period actually depends on the initial angle. 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? The starting angle does not affect the period of a pendulum. Instead, the period is directly affected by the length of the string from which the mass hangs. 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. 5

So Here L=1 m and Time period is not given so we will take it as T only. The Time period does not depend on the mass of the pendulum. so Question-12 : How will friction affect the time period of the pendulum? If friction is present in the medium then it will increase the time period of oscillations because it opposes the force which is acting on the pendulum, In general cases we are not considering the effect of friction because it is so small. If we consider it effects then we will get the time period more than the previous one. Conclusion: Summarize, in a few sentences, the factors which affect the time period of the pendulum. 1. The length of the pendulum L 2. The gravitational acceleration of the planet g 3. Friction or Viscosity which is acting against the driving force. 4. If it is a compound pendulum then moment of Inertia also affects the Time period of Pendulum. , 7