Lab 8: Torque and Statics What to turn in Photo + description of your stack from Part 1 Photo + description of your lever setup from Part 2 O Answers to any questions Team Roles Please choose roles in your lab group and indicate who will be doing each task. If your group has less than 4 people you can have more than one role. Roles Name Director - Coordinates the lab, makes sure all instructions are followed. Technician - Sets up the experiment, records the data, images, etc and distributes it to the group Explainer - This person writes the responses to the questions after discussing with the team. Part 1: Statics and Center of MassPurpose Students will study the static forces in a center-of-mass situation. Theory Seven is the average of 4 and 10, of course. The best way to calculate this is to add the numbers and divide by 2. If another 4 is included, the calculation is then [2.4+1.10]/[2+1]. This is called a weighted average because 4 and 10 are weighted by their quantities. Earth's mass is about 80 times that of the moon, which is roughly 243 000 miles away. A weighted average gives the balance point between them, called the center of mass Xom. If the earth is at zero, Xom = [80.0+1.243000]/[80+1], so about 3000 mi from earth's center. Text The center of mass equation can be easily translated to a calculus form for continuous distributions if every Sm(x)dx sum turns into an integral: . Unsurprisingly, this predicts that the center of mass of a uniform block is Sam at its physical center. The center for a set of identical blocks, however, becomes weighted by their positions: For three of them with centers at 1, 5, and 6 cm, the center is at [1+5+6]/3 = 4 cm.An object won't tip over if its center of mass is directly over a point of solid contact. That is the entire criterion. Procedure The goal of this lab is to find some nearly identical rectangular objects to stack at the edge of a table atop each other farther and farther out until the top-most one has its entire volume out past the edge of the table, and then take a picture of it or measure it. These objects could be paper-back novels, dominoes, playing cards, DVD cases, Jenga blocks, candy bars, sticks of chewing gum, or anything else rigid, rectangulard, and largely uniform. The entirety of the top one must be past the edge of the table, up above thin air. It won't fall off because its center of mass is over the block just below it. This pair won't fall since their common center of mass will be above the block beneath them, and so on down the stack. How many will this take? Find out! If no camera is available to capture this feat, measurements must instead be submitted of the amount the lowest block overhangs the table, the amount the next overhangs that one, and so on. It is easiest to do this from the top down: Get the top-most block to just barely stay on the one below it, then get this pair to just stay on another, and keep going until the goal is reached. It will likely take the form of a curve:Part 2: Torque Purpose Students will explore torque using a simple class-one lever. effort Theory TE load Torque is the cross-product of the radius and force. The cross-product is important because it is an optimizing element for applying torque: Maximize the lever arm, which means the fulcrum radius, maximize the force, and make sure it is applied perpendicular to the lever arm. Figure 20: A class-one lever. The archaic term lever arm is well-chosen. A lever is a torque device. It is one of the fundamental applications of mechanical advantage, called a simple machine. At their core, many devices are really just disguised levers: gears, pulleys, wheel-and-axle systems, crow- bars, pliers, wrenches, door knobs. The pivot-point is what gives it away. For simple levers, the pivot point is called a fulcrum. For a class-one lever, it is between the effort or applied force and the load, which is to be moved. In class-two levers, the pivot is at an end and the load is between. This is how a pry-bar works. In class-three, effort is in between the pivot and load. For all three of them, mechanical advantage is greatest if the effort-force and the load- force are at 90 to the lever arm, which runs along the body of the lever. Since the lever arm out to both forces will always be measured from the pivot, all levers ideally use the same relation: r F = FProcedure 1. Find or make a flat, uniform stick at least 5 in long. Ideally, a wooden ruler or a popsicle stick can be used, or else a strip of box cardboard with constant width cut in the direction of the inner corrugations so it has strength. 2. Measure the length of it and divide by three. Mark the location one-third of the way along it from an end. 3. Place a pen or pencil on a table and set the strip/stick across it at the mark. This is now a class-one lever. The pen or pencil is the fulcrum, and rE = 2rL. 4. Stack pennies or similarly identical units as near to the ends as possible so the lever becomes balanced. Ideally it will take twice as many on the shorter end, but the weight of the lever itself is going to mess this up slightly: The long end is heavier. To compensate for this, the total weight of coins used should be as much as possible without breaking the lever so their weight dominates the system. Don't expect perfection. Analysis Please answer each of the following in Canvas using complete sentences: 1. What was the ratio of FL over FE? It will be unitless, hopefully close to 2. 3 2. Why is it unnecessary to know how much a penny weighs or even the value of g to get this unitless ratio of the one weight force divided by the other