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Project at AISVN
Project at AISVN
Build a Catapult or Trebuchet from cardboard.
Specifications:
- Projectile is a table tennis ball: 2.7 gram.
- Counterweight: 50 gram.
- Height of axle to the ground: 30 centimeter.
For fairness the load arm can't be heavier than the efford arm. The sole source of energy is the potential energy of the counterweight.
Competition
Competition
Which group from grade 9 achieves the longest distance?
Which group from grade 9 achieves the longest distance?
Enter your data into this Google Sheets file!
Enter your data into this Google Sheets file!
Background information
Background information
Comparison of balls:
- Table tennis ball: 2.7 g, diameter 40 mm
- Golf ball: 46 g, diameter 43 mm
- Tennis ball: 58 g, diameter 67 mm
Potential energy of counterweight:
- PE = mgh = 0.05×9.81×0.3 = 0.147 J
Kinetic energy transfered 100% results in velocity
- KE = ½mv² → v = √(2KE/m)
- v = √(2×0.147/0.0027) = 10.4 m/s = 37.6 km/h
Distance calculator
Distance calculator
https://www.omnicalculator.com/physics/range-projectile-motion
https://www.amesweb.info/Physics/Projectile-Motion-Calculator.aspx
Values:
- Velocity: 10.4 m/s
- Angle: 45 degrees
- Height: 0.4 m
Maximum distance:
Maximum distance:
- 11.4 meter
Realistically we can probably transfer only 50% of the potential energy to the kinetic energy. This leaves us with 0.069 Joule and a resulting velocity of 7.1 m/s. Using the distance calculator and a height of only 30 centimeters (the axle) the maximum distance is 5.47 meter.
You want to calculate the maximum distance by yourself? That's great! I created a Jupyter notebook where you can play around with the values and see how it works. Here is the pdf version. The central point is the formula for the distance:
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Weblinks
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