Alpine Gondola Engineering Report 2/24/09 Julia Teitelbaum, Karen Bobkowski, Nick Coury
PURPOSE: Since this semester in Engineering Physics focused on the concepts of force, work, rate, resistance, energy, power, and force transformation, we did the Alpine Gondola project to apply these concepts. In the project, we had to use our understanding of physics concepts to maximize the efficiency of our device. We had to apply the force of the mousetrap over the maximum possible distance, while overcoming the resistance of gravity. We had to use the energy of the mousetrap as efficiently as possible. Although achieving a fast rate of ascension was not the objective of the project, by measuring the time we were able to calculate the rate and power of our device. We transformed rotational mechanical force into linear force applied over a distance.
CONSTRUCTION PROCEDURE We designed our gondola to use the energy in the mousetrap as efficiently as possible. We used a brass rod for an axle and embedded brass washers into the sides of the device. Using metal on metal to minimized the coefficient of friction and so the energy lost there. We used brass tubing and a brass axle and washers because brass is a relatively light metal and still strong. Graphite lubricant further reduced friction in the axle. Extending our bale generated more torque by increasing the lever arm. Using jewelry wire wound around the bale and the tubing to bind the brass tubing to the bale made it very strong and sturdy so that it would not bend, warp, or break while doing work. Styrofoam plates for the drive wheel minimized the mass of the device so that is would travel higher. The Styrofoam plates also helped in construction by creating a groove on the drive wheel for the rope when placed from back to back. We fastened on the rims of two other Styrofoam plates to make the groove narrower to stabilize the device on the rope. We used electrical tape on the axle where the string was attached to increase the torque without making the whole axle thicker and increasing the mass. Although different tape may have been lighter, electrical tape was conveniently available. In addition, the electrical tape was effective in binding the string to the axle. Like the electrical tape, we chose to use polyurethane string because it was light, strong, and on hand. We put electrical tape on the groove of the drive wheel to increase the coefficient of friction with the rope so that the device would grip the rope and not spin out or roll backwards. Using balsa wood to construct the frame of the device reduced the mass while maintaining durability. However, the tendency of the balsa wood to splinter increased the mass because we could not trim as much excess off the sides. Gluing on two Popsicle sticks and seven washers onto one side of the device balanced it to minimize energy lost to wobbling as it climbed the rope, but this did add excess mass. The mousetrap was glued to balsa wood in the
middle of the two balsa wood sides so that we could set it off to one side and line it up with the axle and the drive wheel. We also placed a small basswood block on the same side as the Popsicle sticks and washers to reinforce the joint and further balance out the mass. While our gondola worked well, travelling 1.81 meters up the rope, we could definitely improve upon our design and increase its efficiency.
MATERIALS One Victor mousetrap Two 29 x 3 cm pieces of balsa wood One 7.5 x 8.6 cm piece of balsa wood One 1 x 1 x 4.5 cm piece of basswood Seven of copper 3/16” washers 38 cm of polyurethane string 43 cm of electrical tape Four 15 cm diameter paper plates 40 cm jewelry wire Two 11.5 cm Popsicle sticks 35 cm 0.25 cm diameter brass tubing Super glue Graphite lubricant
SCALE DRAWINGS (ATTACHED) DATA a) Device Mass: 82.9 g b) Diameter of the drive wheel: 15 cm c) Number of powered revolutions of the drive wheel: 5.25 rev
d) Elapsed time for the climb: 3.05 s e) Actual distance climbed by the Gondola: 1.81 m f) Actual height climbed by the Gondola: 0.376 m a. Sin(12)=height/1.81 m b. Height= sin(12)*1.81 m
MODEL ANALYSIS a) Graph of Force vs. Distance from mousetrap calibration lab, including a data table, attached
CALCULATIONS b) Potential Energy stored in the mousetrap (PE): 0.7 Joules a. Given c) Drive wheel circumference: 0.47 m a. Circumference= Π*Diameter i. Diameter = 0.15 m ii. Circumference = Π*0.15 m iii. Circumference = 0.47 m d) Potential Energy gained due to the change of position of the device (U): 0.305 J a. Potential energy = mass*gravity*height i. Mass = 0.0829kg ii. Gravity = 9.8 N/kg iii. Height= 0.376 m b. Potential energy= 0.0829kg *9.8 N/kg *0.376 m c. Potential energy= 0.305 Joules e) Efficiency, based on energy exchanged from the trap to position (Eff): 43.5%
a. Efficiency= Energy out/Energy in i. Energy out (U)= 0.305 J ii. Energy in (PE)= 0.7 J b. Eff= U/PE c. Eff= (0.305 J/0.7 J)* 100 d. Eff= 43.5% f) Average power of the climber (P): 0.10 Watts a. Power= Energy out/time b. P= U/t i. U= 0.305 J ii. T= 3.05 s c. P= 0.305 J /3.05 s d. P=0.10 J/s g) Torque on drive wheel just after it begins to move (Ti): a. Ti= Force* radius of axle i. Force= ii. Radius= b. Ti=F*r c. Ti= h) Torque on drive wheel just before the end of its motion (Tf): a. Tf=
CONCLUSION
We learned how to apply the principles of physics we have been studying to engineer our gondola. We had to cope with real world conditions, applying theoretical principles while dealing with gravity, friction, and constraints on construction and materials. We applied the potential energy stored in the spring of the mousetrap as kinetic energy, and had to change the force to make it useful by attaching the bale to the axle. Building our own axle and drive wheel helped us gain a better understanding of the intricacies of building axles and drive wheels in common rotational mechanical systems. Procuring our own materials helped us realize the importance of cost effectiveness in engineering. The time constraints of the project mirrored real-world deadlines for engineers. By building our own gondola, testing it, and seeing other groups’ gondolas’ successes and failures, we learned how we could apply our knowledge of physics more effectively to make our gondola more efficient. For example, after testing our gondola, we realized that it was possible to build it in a different shape- a triangle. We had to adapt to construction challenges like finding adhesives that would work on metal and Styrofoam. As always, we learned to deal with working in groups to collaborate, which is certainly important since engineers work in groups. Group members had to communicate their ideas clearly and forcefully to our group to get them across and convince other members to try them. We saw firsthand the need to balance directly related values to maximize efficiency. By lengthening the lever arm, we increased the torque, but we could not modify the amount of energy provided by the mousetrap. It was challenging and educational to try to find the optimum length of the bale where it would not be stuck but where it would maximize the torque and the distance travelled by the gondola. We saw the potential for mathematical equations to find the optimum length. From the Alpine Gondola project, we learned applications of physics concepts and solutions to challenges in engineering and building. If we were to do this project again, we would change our design. To start, we would reduce the mass of our device so that more potential energy would be gained in height. We would do this by using a material other than electrical tape to increase the radius of our bale, as the electrical tape was unnecessarily heavy. Furthermore, we would make the sides of the gondola much thinner to reduce the mass since their width was not necessary in the design. This would probably entail using different cuts of balsa wood, but that would not be hard to change. We would also make them longer so that we could lengthen the distance between the mousetrap and the axle and drive wheel to allow for a longer bale. We would increase our torque by further lengthening our bale, since we could have made it longer without the axle being stuck. We would try to use different Styrofoam plates or carve a wheel from insulation foam so that we would not have to improvise to reduce the width of the groove of our drive wheel as we did by attaching the rims of other Styrofoam plates. We would also place the mousetrap in the center of the device so that we would not have to add mass or try to compensate by rebalancing our design. This modification would probably improve the gondola’s efficiency the most. If our design were balanced to begin, we could reduce a large amount of unnecessary mass that was added to balance it. We would be more careful in the
construction of our drive wheel, which was slightly unevenly centered which destabilized the device. We might experiment with a design where the sides of the device would flare out, forming an upside down triangle with the mousetrap as the point and the axle and drive wheel as the base. The inverted triangle design would eliminate the need for the piece of wood in the midsection, further reducing the mass of the gondola. If we used different, specialized adhesives for different parts of the gondola, we could have stronger joints without adding extra mass like the basswood block. Without time or material procurement constraints, we could construct a more effective drive wheel and experiment more to find the optimum design to use the mousetrap’s energy efficiently. _