Challenge: To design a crane that can support a load of at least 50 grams as far as possible from the edge of your desk.
Parameters: The crane consists of all parts of your construction EXCEPT the load. The total mass of your crane cannot exceed 750 grams. It's base can be a maximum of 20 cm long and 20 cm wide, square to the edge of the table. It cannot attach to the desk in any way, must contact only the top of the desk, and must be stable while loaded or unloaded. The width of your crane from front edge of base to rear of counterweight or counterweight arm cannot exceed the width of the desk (about 75 cm).
Scoring: Your crane will be scored based on the following formula:
Score = load mass (in grams) * load lever2 (in meters squared)
The load cannot be less than 50 grams. The load lever will be measured from the front edge of the desk to the centre of the load mass, horizontally. Rank will be based on score, with highest score earning highest rank.
Physics: The centre of mass of your unloaded crane, and the mass of your unloaded crane, can be used to determine the counter-torque provided by your crane. If perfectly balanced on the back edge of the base when unloaded, and if your base is 20 cm, the centre of mass of your crane is 20 cm from the front edge of the table! When loaded, and perfectly balanced on the front edge of the desk, the torque caused by the load will match exactly the counter-torque provided by your crane when it has only 20 cm of leverage.
Extensions: The theoretical maximum score would be 450 gm2. Can you show how that is calculated? What hints does that give you about the design of your crane?
Help/Hints: You want to use the maximum 20 cm allowed for the base. Think about light materials that can be used to make long levers. Make sure you plan for flexing by building up a light, stable base, or by using piers and string for example. Look at pictures of real cranes for some ideas.
Quiz Topics: Equilibrium
Online Text: chapter 9