Lab04_Conservation-of-energy

PHY 110 Lab Exercise Lab 4: Conservation of energy Note that for the online version of this lab exercise, data will be provided and students will NOT need to obtain the equipment listed. This equipment list and data collection instructions are provided so that students understand how the data was generated. Purpose To test whether or not conservation of energy is true for a pendulum. Equipment used A ring stand, a clamp with rod, string, a “photogate pendulum set,” a photogate timer on a photogate stand, a Vernier caliper, a ruler, and a meter stick. Background When a pendulum is pulled aside so that the pendulum bob is a height h above the bottom of its swing, all its energy will be initially in the form of gravitational potential energy. After the pendulum is released, it will have a speed v at the bottom of the swing due to the transfer of some potential energy to kinetic energy. The conservation of energy equation gives ½ mv 2 = mgh , or more simply: v 2 =2 gh . Procedure and Data In general, three different pendulums, made from different materials, are available for use in this experiment. Choose one and record your choice. Choice of pendulum: _Aluminum_ The first step is to measure the width w of the selected pendulum using the Vernier caliper. This will be used later to calculate the speed of the pendulum as it passes through a photogate, which measures the time it takes, t , for the pendulum to pass through. The speed of the pendulum will be found using the formula v = w / t . Width of pendulum: w = 1.58cm It will work best to convert the width you measured into meters: Width of pendulum: w = 0.0158 m

Set up the equipment so a pendulum hangs from the string in such a way that it blocks the photogate timer as shown to the right. Determine the length of the pendulum by measuring the distance between the top where the string is secured and a point in the middle of the pendulum bob. Record the length of the pendulum, L : L = 60.2 cm Then, remove the photogate temporarily to determine the height of the center of the pendulum above some reference point (probably the tabletop), h f . Be sure to record your result in units of meters, not centimeters. h f = 0.076 m Put the photogate back into place. Plug the photogate connector into the first digital channel of the Science Workshop interface box. Run the Capstone software. Your instructor will explain how to set up the software to use the photogate to determine the time t for how long it takes for the pendulum to move across the photogate. You will perform seven trials for each part below. In each trial, pull the pendulum to the side so that it starts at different heights h 0 . Record the height h 0 in the second column of the table. Release the pendulum from rest and record the time t that the photogate timer records in the third column. Use this information to calculate v using the formula v = w / t , and record the values in the fifth column. Then, square the quantities recorded in the fifth column to fill in the column labeled v 2 . trial h 0 h = h 0 – h f t v = w / t v 2 = ( w / t ) 2 1 0.122 0.046 0.0162 0.975308642 0.9512269471 2 0.16 0.084 0.0117 1.35042735 1.823654029 3 0.227 0.151 0.0088 1.795454545 3.223657025 4 0.315 0.239 0.0073 2.164383562 4.684556202 5 0.37 0.294 0.0063 2.507936508 6.289745528 6 0.445 0.369 0.0057 2.771929825 7.683594952 7 0.567 0.491 0.0054 2.925925926 8.5610425524 Analysis You will plot v 2 versus h = h 0 - h f . If the relation v 2 =2 gh is true, then you should get a line with slope equal to 2 g = 19.6 m/s 2 . An Excel spreadsheet is embedded in this document for you to plot v 2 versus h ; that is, to plot v 2 on the vertical axis and h on the horizontal axis. To use it, double-click on the spreadsheet image. Once it is active, enter the time and displacement data in the spreadsheet cells, and the graph will be updated automatically. An equation of the best fit line through the data will appear in the graph. The value multiplying the “x” in the formula gives the slope. Clicking outside the Excel spreadsheet area will return control to the Word document.