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Transcript
ProCSI Hands-On Activity Day 1: Engineering Measurement Lab Introduction Physics is defined as “the study of matter and energy and their interactions.” It is a set of laws that describes everything around us and dictates how things interact. For example, Newton’s 2nd law of motion is known as “the law of resultant force” and states that the rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction. This definition probably doesn’t make a lot of sense and may be confusing so let’s break it down and look at each part. Momentum, also known as inertia, equals mass times p mv velocity where ‘p’ is momentum, ‘m’ is mass, ‘v’ is velocity (speed) and the arrows indicate that direction is important. When objects are sitting still they have no momentum and when they are moving, they have a momentum of mass times velocity. A Major League baseball weighs about 5 ounces, where the average bowling ball weighs about 15 lbs. This means a bowling ball has about 48 times the momentum of a baseball when they are moving at the same speed. In order to change an object’s momentum (i.e., to stop the baseball’s movement) you have to apply a force that counteracts the momentum of the object. To throw a baseball at 40 mph, a force is applied to the ball during the throw which gives it a certain amount of momentum. To stop the ball, an equal and opposite force has to be exerted on the baseball (minus the aerodynamic drag) to counter-act the momentum. Figure 1: A baseball’s momentum is the product of mass times velocity Mathematically, Newtons’ 2nd Law can be expressed as: F ma , where ‘F’ is the force (the arrow above means that direction is important), ‘m’ is the mass, and ‘a’ is the acceleration. If you caught a bowling ball with 48 times the momentum in the same way that you caught the baseball (i.e., accelerate the ball to a stop at the same rate), according to the equation it would take 48 times the force to do this! Although you don’t have to be an engineer to know that playing baseball with a bowling ball isn’t a great idea, engineers can solve a lot of interesting problems by knowing that the laws of physics always apply and how they work mathematically. For example, if you wanted to build a train that travels at 200 mph, how powerful does the engine have to be? Can it travel on regular train tracks or do special track needs to be designed? How about if you wanted to drop a 500 lbs. crate of food out of an airplane, how big does the parachute have to be so that the crate doesn’t break when it hits the ground? An engineer uses their knowledge of physics and math to overcome these types of challenges during each and every design process. Today, we will be testing the so called “laws” of physics. By setting up simple experiments and taking measurements we can verify that important physical laws such as Newton’s 2nd law are mathematically correct. We will start with a simple ‘system’ that only has 1 force applied to it. This ‘system’ is a ball that drops due to the force of gravity. We will use Newton’s 2nd Law and the Law of Gravitation to indirectly measure the height of the 2nd and 3rd floor of the Mechanical Engineering Building, and prizes will be awarded the groups whose measurements are the closest to the actual heights. The second experiment is more complex, with up to 3 forces applied to the system at a single time. This system is called a mass-spring-damper; variations of this type of system are commonly found in our everyday lives. Experiment 1: Newton’s Apple Background Some of you may be familiar with the story of Newton’s apple, where the famous scientist Isaac Newton was inspired to investigate gravity when he observed an apple falling from a tree. One version of the story says that he actually got hit in the head by the falling apple, and the blow to the head inspired his work on gravitational theory. Figure 2: Newton’s Apple He would eventually write about universal gravitation in his famous manuscript “On the motion of bodies in an orbit” (originally titled in Latin as De motu corporum in gyrum), which explains how gravity affects the way planets and moons orbit each other. Although Newton wasn’t the first person to investigate the idea of gravity (Galileo was the first), it is the story of the falling apple that is the inspiration for the first lab. We will use a ‘falling apple’ (a tennis ball in this case) to measure various heights. Motivation Use experimental measurements in conjunction with Newton’s 2nd law and the Law of Gravity to calculate a desired quantity. Verify that the force of gravity is constant over small vertical distances, and that Newton’s 2nd Law still applies after being extended using math. Procedure Each team will be given a stopwatch and a tennis ball. To find the time required for the ball to drop to the ground, start the stopwatch when the ball is dropped, and stop it when the ball hits the ground. Repeat this experiment ten times and average the results to find the average time required for the ball to drop to the ground. We will use this value with the physical laws discussed earlier to derive the height of the 2nd floor railing. Repeat the procedure to determine the height of the 3rd floor railing. For each height measurement, the team that is closest to the actual height wins (one winner for each height measurement). Experiment 2: Mass-Spring-Damper System Background Mass-spring-damper systems are extremely common in engineering. From its title, there are three types of force elements involved in the system: masses, springs, and dampers. An engineering representation of this system can be seen below, where m is a mass, k is a spring, and B is a damper. Figure 3 shows a ‘translational’ mass-spring-damper system, where translational just means that it moves in a straight line. A few real life examples of mass-spring-damper systems include: the suspension and tires of cars or trucks, muscles and tendons in your body, and tuned mass dampers in tall buildings. Figure 3: An engineering representation of a translational mass-spring-damper system Figure 4: Taipei-101’s tuned mass damper (top), and its placement in the building (bottom) Motivation Use a computer to do measurements on a complex system to verify that it obeys Newton’s 2nd law just as simple systems do. Observe the free response of a single degree of freedom mass-spring-damper system, and how its response changes as the mass is varied. If time permits, extend lab to two degrees of freedom. Procedure We will be observing a mass-spring-damper system with “Position vs. Time” plots, which are automatically created by the data acquisition software. Note that the plots created during the activity have position units of ‘encoder counts’. These values can be easily converted into an actual length value by using the conversion value in Table 1. We will only be using the mass and spring on the rectilinear (translational) system with the damper deactivated; a small amount of damping will be present due to friction. Some of the plant specific information can be seen below in Table 1. Spring Stiffness (k) 770 N/m Mass of Weights (M) 0.59 kg (each) Mass of Cart (Mc) 0.5 kg Mass of Motor (Mm) 0.34 kg Encoder conversion 2038 counts/cm Table 1: System mass, stiffness and encoder values Figure 5 below shows a rectilinear system similar to the one used in this activity. Figure 5: A rectilinear system Figure 6 shows a schematic representation of the system with only one mass carrier. The system shown above in Figure 5 has three mass carriers. Figure 6: Translational mass-spring-damper system used in this activity The damping coefficient c in Figure 6 is unknown for these systems and must be determined from experimental data. This will be done for you and details of the process can be explained upon request (or try doing an internet search for “Logarithmic decrement”). The serial logger application should already be running on your group’s computer when you begin the lab. See the instructor for assistance if this is not the case. LabView Serial Logger Interface Settings Baud Rate: 115200 Sample Rate: 250 Hz Number of Samples: (Variable) Position/Velocity Goal: 0 Read Variable 1 Name: Position There are no write variables for this lab. For each experiment, perform the following steps: Inspect the Equipment 1. Inspect the system. Make a diagram of its components and note how the position of the mass carrier is measured. 2. Observe how the system moves by displacing the mass carrier approximately 3 cm in either direction and releasing it. 3. Observe how the Position vs. Time plot depends on the starting position of the mass carrier. Set the “Number of Samples” to a value which will record 10 seconds of data. Be sure that the “Save Data” button on the bottom is turned off. First, press the “Run Experiment” button, then move the mass carrier 3 cm in either direction and release it. Second, move the mass carrier 3cm in either direction and hold it at that position. Have a teammate press the “Run Experiment” button, and then release the mass carrier. Observe the differences. Run the Experiment Note: Be sure to press the “Run Experiment” button first, and then displace the mass carrier to its starting position. This ensures that the position vs. time plots will settle at zero. 1. We want to save our data for later use, so be sure the “Save Data” button is turned on. Begin the first trial by making sure there are no masses on the mass carrier. 2. Press the “Run Experiment” button, displace the mass carrier 3 cm in either direction, and then release it. 3. When the data acquisition software has logged the data, it will prompt you to save the file. Give the data file a name that makes it easy to identify which experiment it represents, and save it in the folder labeled “ProCSI” which can be found on the desktop. 4. Add one mass block to the mass carrier, and run steps 2-3 again until there are four mass blocks on the mass carrier.