Challenge:
To design a constant mass system of two objects, connected by a string over a pulley, which will accelerate at a desired rate when released from rest.
Criteria:
The horizontal and vertical portions of your system must accelerate together, so must be attached by strong, inflexible thread or string. They cannot damage the desk in any way. The pulley can be your own or one of mine, but if it is one of my pulleys, it cannot be removed from the room. The horizontal portion cannot exceed 15 cm in the horizontal dimensions, and must have a vertical flag or fin that is exactly 10.00 cm long and 5.0 cm high, attached so that the overall height is between 14 cm and 16 cm. This flag is what will be measured during the competition to find your acceleration. You must design your system so that you can change the acceleration simply by moving mass between the two components, such that the total mass of your system remains constant. Your system should be able to achieve any acceleration between 3.0 m/s2 and 7.0 m/s2.
You will be given one try with the photogate at a random acceleration, then a different contest target acceleration will be set and Mr. J will test your system with three trials for an average. You can adjust your system after the practice one, but you cannot during the three contest trials.
Scoring:
Score = | Your acceleration – Target acceleration | ÷ Target acceleration
Physics:
The force of tension in your string is very difficult (impossible?) to measure during acceleration. Luckily those forces are internal to your system, so can be ignored if you treat the horizontal and vertical portions as one rather strange object. The mass of the system is constant and can be measured accurately. You just have to make sure you don’t accidentally lose pieces! Your system will accelerate faster if you distribute more of the fixed system mass to the vertical piece, and vice versa if you put more of the mass on the horizontal piece. You need to be able to move about 75% of the mass between the two pieces of your system or you won’t be able to achieve the full range of accelerations. Friction is a force that is external to the system and it will definitely affect the acceleration you achieve. The more friction you have in your system, the harder it will be to attain your slower accelerations, and they will be more inconsistent.
Extensions:
Once you have calculated the force of friction and acceleration you can then calculate the force of tension in the string at that acceleration. Newton’s Laws of Motion apply to rotation, not just translation, so heavy pulleys and wheels are a significant factor in the acceleration, and should be avoided, unless you really, really like math!
Help/Hints:
Do a really good job of the flag, and use video analysis to get the times needed for the acceleration calculation. Make the mass objects transferrable, countable, and uniform to make easy data analysis. (Weighing every time could be very frustrating!) Graph your results and determine the equation of the graph so that you can calculate exactly how much mass to transfer for the competition.
Quiz Topics:
Kinematics in one dimension, constant acceleration, Newton’s Laws of Motion, Free Body Diagrams.
Online Text:
2.4 – 2.8, 4.3 – 4.7 (only one dimension questions!)
Timeline:
Day 1 Planning
Day 2, 3 Building
Day 4, 5 Calibrating
Day 6 Competition