Challenge: To design a controllable device that mimics an elevator with a constant slow velocity.
Parameters: Your device must raise an 18 cm by 4.2 cm diameter cylindrical object from the floor to the power post near the ceiling at a constant slow velocity. You will be told the target velocity, and will have 2 minutes to start the motion. The target velocity will be a value between 15.00 cm/s and 25.00 cm/s. Your device must fit an imaginary 20 cm cubic anchoring spot on the back of the power drop-down, measured from the ceiling. Your power supply must be a DC adaptor rated 9.0 V or less. The cylinder must be started from rest and must travel freely at least 10 cm before the leading edge arrives at the first photo gate. The photo gates will be set up to measure your cylinder’s average velocity over a 2.0 m displacement, and an instantaneous velocity either at the 1/3 point or at the 2/3 point at Mr. J’s discretion. Please do not alter or damage the cylinders.
Scoring: Ensure that Mr. Jamieson checks the height of your cylinder first. You will have five minutes for the competition. For scoring we will take the average of your instantaneous velocity and your average velocity, plus we will find the difference between those two velocities. You want to hit the target velocity dead on, and you want both estimates of actual velocity to match each other perfectly!
Cylinders that don’t trigger a photo gate will be counted as zero velocity. It is up to you to design your device to move the cylinder in as straight a line as possible. The lowest score will receive the highest rank. In the unlikely event of a tie, the lower power adaptor will be the winner.
Physics: Your winch must allow a fast-spinning DC motor to turn a drum slowly so that your cylinder can be moved slowly. This will require reducing gears or pulleys or something like that. To be as constant as possible, you want to reduce sources of friction, and may want to provide some rotational inertia (flywheel). In order to maintain a constant velocity, the forces acting on your cylinder must be completely balanced. A rheostat (variable resistor) is an excellent way to control the speed of your motor, but remember that motors work better at higher rpm.
Extensions: The velocity measured at the photo-gate is called instantaneous, while that calculated from displacement and time interval is called average. If your device moves the cylinder at a constant rate, the two velocities will be the same. If your device is really well designed, it should be able to lift OR lower the cylinder at the same constant velocity, but we will only expect you to lift it.
Help/Hints: To measure velocity you can fix a meter stick behind the path of the cylinder and use video analysis to get average velocity data. To get an instantaneous velocity, you can do a close-up and time how long it takes to pass a fixed point of reference. Use lots of light!
Make a scale on your variable resistor, or whatever method you are using to adjust the speed of your device, and graph your data from your calibration attempts.
Quiz Topics: Kinematics in one dimension
Constant velocity, average velocity, instantaneous velocity.
Force Concept, Free-body diagrams, Newton’s First Law, Simple machines
Online Text: 2, 4, 7.2, 9.3