Exact Velocity Pendulum

Challenge: To design an adjustable pendulum that can achieve an exact velocity through a photo gate after release from an elevated position.

Parameters: The pendulum must not strike the photo gate. It must be released from rest and pass through the photo gate at its lowest point. The lowest point of your pendulum must be between 10.0 and 15.0 cm above the table surface. I must be able to position my photo gate and measure your pendulum width while it is hanging at rest at its lowest position. During the contest trials, you must prevent the pendulum from returning to the photo gate after its initial pass.

Scoring: There will be two target velocities between 2.00 m/s and 4.00 m/s, and you will get up to three tries at each velocity within a five-minute time limit. Striking the photo gate will be recorded as a penalty. The best attempt for each velocity will be used for the scoring.

Score = (∆v₁ / v₁) * 100% + (∆v₂ / v₂) * 100% + n

v is the target velocity, ∆v is the absolute difference between your velocity and the target velocity. n is the number of times you hit the photo gate. Please don’t hit the photo gate. Rank will be based on score, with lowest score earning highest rank.

Physics: The pendulum will have potential energy while raised, which will turn into kinetic energy (and a tiny amount of heat) while it falls to its lowest position. The velocity at that position can be estimated from the change in height of the centre of mass of your pendulum. The dropping pendulum loses gravitational potential energy (∆E_p = mg∆h) and gains kinetic energy (E_k = 0.5mv²). The photo gate measures the time your pendulum blocks the light, so the velocity will be calculated by dividing the width of your pendulum by the time. v = ∆x/∆t

Extensions: The less friction there is, the easier it will be to relate your velocity to height change mathematically.

Help/Hints: You can find your velocity by taking a video of something bright as the pendulum passes in front. Knowing frame rate, you can find time. From width and time, you can find velocity. Releasing by hand WITHOUT imparting an initial velocity is quite difficult. Try using a thread for example. Use video to troubleshoot problems with your pendulum’s motion. 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 high to raise your pendulum to achieve the target velocity during the contest.

Quiz Topics: Energy, Work and Power

Online Text: 9.1, 9.2