Challenge: To design an adjustable, spring-loaded launcher that can shoot a projectile horizontally off your desk to hit a target on the floor.
Parameters: The launcher must be able to launch a spherical projectile of between 5 and 50 grams and 10 and 30 mm diameter (for example a marble or ball bearing) using only the energy stored in a spring. The launch device must have a trigger to release the projectile horizontally from the device. The structure you build cannot project beyond the edge of the table and cannot release the projectile more than 5 cm above the table.
Scoring: You will be told the target location and will have 5 minutes to arrange your launcher to hit the target. The target location will be somewhere between 60 cm and 90 cm from the edge of your desk, measured horizontally on the floor. You will get up to three attempts in that time limit, and the best attempt will be used for the score.
Score = (∆x / x) * 100%
x is the position of the target measured horizontally from the edge of the desk ∆x is the distance between the target and where your projectile first lands.
Rank will be based on score, with lowest score earning highest rank.
Physics: Unbalanced force applied by the compressed spring onto the projectile causes acceleration according to Newton’s Second Law. The force is proportional to the compression distance, so the force would decrease during the launch. Therefore the acceleration is not uniform. Spring forces can be modelled mathematically in relation to compression distance. The spring has mass (inertia), and therefore “accelerates itself”. Accounting for this is not impossible, but quite difficult!
Extensions: Help/Hints: Calibration of your device (recorded practice!) can give you a good idea of its precision and accuracy, and help you determine how to adjust it. Graph your calibration data and draw a line of best fit. Use the fit line to find out how much to compress your spring during the contest. i.e. Once you are given the target distance, look at your calibration graph to determine how much to compress the spring.
Quiz Topics: Constant Acceleration in One Dimension, Intro to Projectile Motion. Newton’s Laws. (Unbalanced Forces Cause Acceleration)
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