Winch Challenge

Challenge: To design a motorized winch that can pull a wooden block across the floor at a constant target velocity.

Parameters: Mr. J will place a small paper card on top of the centre of your block and fasten it with tape. The added mass will be negligible. You will be told the target velocity, and will have 2 minutes to tune your system, but not start it. The target velocity will be a value between 10.00 cm/s and 20.00 cm/s. Your winch should fit a 15 cm by 15 cm footprint area located 30 cm past the finish line. Your power supply must be a DC adaptor rated 9.0 V or less. I will use an ammeter and voltmeter to measure the power consumption of your device during operation. See diagrams below. The block must be started from rest and must travel freely at least 10 cm before the leading edge arrives at the starting line. My photo-gates will be placed somewhere near the 1/3 and 2/3 marks of a three meter long “course” to measure the instantaneous velocity of your block at two locations.

Scoring: For scoring we will take the average of your instantaneous velocities measured by the two photo gates as your average velocity. That will be compared against the requested velocity to find percent difference. The difference between the two instantaneous velocities should be as little as possible. Your score will be based on following formula:

| % difference v | + | v₁ - v₂ | + log (P in W)

The lowest score will receive the highest rank. The logarithm of the power in Watts would be a score around zero for motors using around one Watt. The lowest score will receive the highest rank.

Physics: The floor is not perfectly smooth or flat, so it is important that your winch has a large mechanical advantage (pulleys or reducing gears), and/or some rotational inertia (flywheel). In order to maintain a constant velocity, forces acting against the motion of your block must be exactly balanced by the forward tension force in your string. A rheostat (variable resistor) is an excellent way to control the speed of your winch. A piece of NiChrome wire can be used as a variable resistor.

Extensions: The velocity at one moment in time is called instantaneous, while that calculated from displacement and time interval is called average. If the winch pulls the block at a constant rate, the two velocities will be the same.

The physics of friction is very, very complicated.

Help/Hints: Use video analysis to get accurate velocity data. Use lots of light!

Make a scale on your variable resistor, or whatever method you are using to adjust the speed of your winch, 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

Online Text: 2.1 - 2.3, 4.1, 4.2 (concepts only), 20.1-20.4 (20.3 concepts only), 21.1-21.3 (only easiest questions)

Timeline: Day 1 Planning

Day 2 Building

Day 3 Building

Day 4 Calibrating

Day 5 Calibrating

Day 6 Contest

The wires from old heating elements, toasters, toaster ovens, irons, etc. are usually made of NiChrome, which would make an ideal variable resistor for this project. Here is what the circuit diagram looks like for a variable resistor that can control the speed of a motor.