Lab 7

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School

Columbus State Community College *

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Course

1250

Subject

Mechanical Engineering

Date

Apr 3, 2024

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pdf

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Uploaded by HighnessPony3347

5t?,e:7 LAB 7: WORK AND ENERGY Introduction The experiments in this lab investigate energy and how it's transformed from one type to another. We'll focus on just two types of energy: kinetic energy (K) and gravitational potential energy (U). Their definitions are and K = 1 mv 2 2 U=mgh 7.1 7.2 Work transforms energy from one type to another. The work done on an object by a constant force is calculated from this relationship: W=Fdcos¢ 7.3 When a force varies with time, the work it does can be calculated by making a graph of Fcos¢ vs. d; the area under the curve is equal to the work done. There are two ways to use energy to predict what a body subject to a set of forces will do. In general, when a net external force does work Won a body, the resulting change in the body's kinetic energy is found from the work-energy theorem: W=M 7.4 In words, the net work done on a body during any time interval is equal to the change in its kinetic energy L1K - K, K,. The key word here is net; equation Error! Reference source not found. doesn't apply to any single force acting on a body, unless all other forces balance out. A second predictive method uses the principle of energy conservation. When non- conservative forces (friction, air resis~ance, normal forces) do no work on a body, then its total mechanical energy remains constant. Total mechanical energy Emec is defined as Emec =K +U 7.5 There are two equivalent ways to formulate the conservation principle mathematically: 7.6 and /J..U=-M 7.7 The first version compares the net mechanical energy at two different instants and predicts that it's the same at both: E 1 = E 2 . The second version explicitly claims that, when mechanical energy is conserved, any gain in U is offset by a loss of K, and vice versa. 63

PRELAB QUESTIONS Lab 7: Work & energy Name: J)~/2Al1 :;3.orD 1. In Experiment I, suppose the average tension is 0.51 N over a displacement of 1.1 m. The work done by tension during that displacement is ~~56j) b. 1.7 J C. 2.4 J 2. In Experiment I, suppose the falling mass is m = 156 g, and the total mass of the sensor, carts, and load is M = 1239 g. During one trial, the initial and final speeds are 0.36 m/s and 1.29 m/s. The change in the carts' kinetic energy for this trial is a. 0.62 J C. 1.7 J 3. Before pressing the TARE button on the force sensor, you should be sure that the string attached to its hook is taut. ~ALSE 4. In Experiment II, suppose the final speed of the masses is 3.1 m/s, and mA = 455 g, m 8 . = 412 g. The system's final kinetic energy is a. 1.5 J b. 2. 7 J cg 5. In Experiment II, mass l's potential energy change is negative, and mass 2's potential energy change is positive. cg FALSE 64

Experiment I: Work & Kinetic Energy In this experiment, a mass hanging from a string running over a pulley accelerates two carts. According to equation Errorl Reference source not found., the work done by tension should equal the carts' change in kinetic energy. Does it? Equipment 2 carts with Velcro pads 2.2 m dynamics track with bumper and pulley 4 table rods 2 right-angle clamp assorted masses ( ~1 kg) string and scissors force sensor motion sensor mass hanger, assorted masses Setup Mount the track on four table rods, using track clamps to hold it in place o the end of the track should project over the end of the lab table o the track should be 1-2 m above the floor Install a bumper near the end of the track over the floor Attach a pulley to the same end of the track as the bumper Clip the motion sensor to the opposite end of the track o set its switch to the "narrow beam" position Level the track Screw in the hook to the force sensor, if necessary Recalibrate the force sensor for positive force readings, if desired o see Appendix C or the instructo~ Attach the force sensor to one cart Attach the two carts together by their Velcro pads Place a total load of 500-1000 g in the carts Measure and record M, the total mass of the carts, sensor, and load o for simplicity, M will be referred to as "the mass of the carts" from now on Place the carts on the track with the force sensor hook facing the pulley o hold or block the carts while getting ready Tie a string to the hook and run it over the pulley Tie a mass hanger to the free end of the string Adjust the string's length so the carts can roll roughly 1 meter (or more) before o they reach the bumper o the mass hanger hits the floor Check your setup to make sure that o the motion sensor is aimed at the carts and set to "narrow beam" o the force sensor's cord won't get hung up on anything A diagram of the equipment setup appears on the next page. 65

Equipment setup: bumper force sensor & carts (M) motion sensor falling m mass table rods ------ 7 Computer setup Open DataStudio and choose Create Experiment Select Force Sensor and Motion Sensor from the Sensors menu Connect both sensors to the data interface as shown Set the sample rate to at least 20 Hz (same for both sensors) Open a single Graph, and use it to plot o force vs. position o velocity vs. position Lock the graph's horizontal axes with the ~ii button o if you use separate graph windows, the lock button won't work Procedure Roll the carts back until they're about 15 cm from the motion sensor Make the string slack, then press the force sensor's TARE button Holding the cart in place, put 100g on the mass hanger Get someone in position to catch the cart before it hits the bumper Make sure the string is horizontal Click Start Release the carts Click Stop and catch the carts before they hit the bumper If the data on either graph look bad, run the trial again If the graphs show good data, then o measure and record m, the total mass hanging from the string o add 50 g to the mass hanger and repeat Run a total of five trials with increasing m's o M doesn't change; it's the mass of the sensor, carts, and load NOTE: It's important to zero the force sensor before every trial. Be sure that no force acts on the force sensor when you press TARE. 66

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