Fnu Sheron Brayan Sanchez Zehao Wang Lab 6: The Simple Pendulum Trial 1: L1: 25cm Trial 2: L2:20cm Trial 3: L3: 15cm Trial 4: L4: 10cm Trial 5: L5: 5cm Lab07-Simple-Pendulum Lab 7: The Simple Pendulum...

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Fnu Sheron Brayan Sanchez Zehao Wang Lab 6: The Simple Pendulum Trial 1: L1: 25cm Trial 2: L2:20cm Trial 3: L3: 15cm Trial 4: L4: 10cm Trial 5: L5: 5cm Lab07-Simple-Pendulum Lab 7: The Simple Pendulum Objectives • Determine the acceleration due to gravity at your location using the period oscillation of the IOLab device hang by a string. Physics Overview A simple pendulum, which consists of a particle of mass m (called the bob of the pendulum) suspended from one end of an unstretchable, massless string of length L that is fixed at the other end, as shown in Figure 1(a). In a simple pendulum, the only forces acting on the mass are the force of gravity Fg and tension T as shown in a free body diagram (Figure 1(b)). The component of the gravitational force, restores the mass to its equilibrium position ( will always point toward the equilibrium position Figure 1(b)). Rotational form of Newton’s 2nd law: where are torque and angular acceleration. (Figure 1(b)) ( , moment of inertia of a particle) This does not represent a Simple Harmonic Motion (SHM). However, for small angles it becomes an equation for a SHM: The period of this motion, T, is the time it takes for the mass to complete 1 full cycle. This is shown in Figure 2. We can use the known values of T and L to calculate acceleration due to gravity g at your location. mg sin θ mg sin θ τnet = Iα τ and α τnet = − (mg sin θ )L Iα = I d2θ dt2 ⇒ I d2θ dt2 = mL2 d2θ dt2 = − mg sin θ L ⇒ I = mL2 d2θ dt2 = − g L sin θ sin θ ≈ θ d2θ dt2 = − g L θ, ω2 = g L , T = 2π L g PHYS 4A Summer 2020, IVC 1 Figure 1 Figure 1 Figure 2 Procedures 1. Attach the IOLab device to a cord or string. Measure the length of the string using a ruler. Call it L1. Measure the length of the cord 5 times. 2. In the IOLab software, select the Force Sensor. 3. Hang the combined system (IOLab device and cord) as shown in Figure 1(a). 4. Push the device slightly as shown in Figure 1(a). 5. Using the force versus time plot, measure the time between the first 5 peaks in the oscillations. This will represent 4 periods. Divide this time by 4 to find the period. 6. Repeat the above period measurements 5 times. 7. Repeat the period measurements by attaching the IOLab device to a longer cord L2. That is L2 > L1. Repeat this measurements 5 times. 8. Calculate the periods for the two pendulum lengths L1 and L2 (for the 5 trial measurements). 9. Using the period measurements, calculate the value of the acceleration due to gravity using the equation (derived from ). Find the mean value of g from the 5 trials and the two lengths L1 and L2 Error Analysis 1. Find the error of measurement of the strings. 2. Find the error of measurement of g. Error propagation: The errors of measurements of length and period propagate to be an error acceleration due to gravity estimation. Lab Report What to include in your lab report • What is the objective of the lab? • What are the devices used? • Describe the results of the experiment. • Present graphs of force versus time for the 2 lengths L1 and L2 (1 trial each). • Present the period measurement in tabular form (for 5 trials) for lengths L1 and L2. • Describe how the acceleration due gravity estimation is made (using one length). • Using the 5 trial measurements, determine the average value of the acceleration due to gravity — for each length. • Discuss the errors of measurement. • Questions to answer 1. Does your data show the dependence of the period of a simple pendulum on its length? 2. Does the period of a simple pendulum depend on the mass of the bob’?. 3. Compare the measured acceleration due to gravity with a theoretical acceleration due to gravity. • Summary and Conclusion g = 4π 2 L T2 T = 2π L g PHYS 4A Summer 2020, IVC 2 Fnu Sheron Brayan Sanchez Zehao Wang Lab 6: The Simple Pendulum Trial 1: L1: 25cm Trial 2: L2:20cm Trial 3: L3: 15cm Trial 4: L4: 10cm Trial 5: L5: 5cm