Physics Olympics: Detailed Rules

The Leonardo da Vinci Softball Catapult Contest
Mousetrap Car Race
Spontaneous Event
Egg Drop
Fermi Questions
Electromagnet
Bridge Build
Quiz Show

The Leonardo da Vinci Softball Catapult Contest
A small Italian city-state called the UNT Physics Department has decided that it needs to buy several softball catapults as siege weapons. The
physics department contacted the famous military engineer and physicist Leonardo da Vinci to design and build the catapults but he is presently on vacation relaxing with his hobby (painting a portrait of some lady by the name of Mona). Therefore, the department has decided to hold an open design competition. Each design team is to design a softball catapult and to build a prototype that will be demonstrated at the UNT Physics Department during the 1999 Physics Olympics. The rules for the competition are as follows:
Design:
The catapult must be completely mechanical in design. The use of compressed gases or electricity is forbidden. No slingshots are allowed.
Scoring for Competition
The scoring for the competition will be the sum of the scores for the following four criteria.

1. Test:
   The catapult must be set up before entering the test area. The catapult is to fire a softball (supplied by UNT) at a target forty meters away from the catapult (see Figure 1). The team will be given five minutes to make two practice throws and any adjustments needed. You will then be given ten minutes to make the three attempts. The score for good throws on the test will be based on the following formula: where __R is the distance between where the softball lands and the target and T is the total time the softball is in the air. Any throws in which the softball travels less than 10 meters will be considered failures and no score will be given since it would kill our own physicists. The best result of the three attempts will become the test score for the group.
2. Quality of Prototype:
   We want to make sure that your group could produce quality catapults. A judge will give you a score of 0 to 10 on the quality of your
   prototype. Some concerns of the judges are:
   1. Quality of Construction -- Is the catapult going to fall apart after it is used? Was Quality really Job One?
      
   2. Flexibility -- Is the catapult mobile so that we can move it? How easy is it to adjust the range of the catapult?
      
   3. Practical Design -- Could this catapult really work?
      
   4. Aesthetics -- Is the catapult nice to look at?
   5. Manufacture Specifications:
      We want to make sure that you can build all the catapults with the same specifications. We wouldn't want one catapult to shoot 30 meters and another to shoot 50 meters. Thus, we require your team to predict the outcome of your catapult's test. You must supply the judges with the following results that you expect your catapult to achieve:
      1. Range of Catapult
         
      2. Time that softball will be in the air
         
      3. Maximum angle of wall that catapult can fire over
         
      4. Angle at which softball will be fired
         
      5. Muzzle velocity of softball

      After test firing, the judges will compute these quantities for your best throw. You will receive a score from 0 to 10 based upon the following rules for all five specifications:

      1. If a test result matched a specification to within 15%, you get 2 points for that spec.
         
      2. If a test result matched a specification to within 30%, you get 1 point for that spec.
         
      3. If a test result was more than 30% away from specification, you get 0 points for that spec.
3. Theoretical Understanding of Projectile Motion:
   We want to make sure that you understand your catapult and the principles behind throwing softball projectiles so that you could build
   more catapults that work. The judges will therefore select one or more team members to answer some questions about projectile motion and how they used this in their catapult's design. (Every member should know how their catapult works and about projectile motion since you could be chosen by the judges!!!) Example questions might include:
   1. What was the maximum height that your softball obtained during your best throw?
      
   2. Calculate the muzzle velocity for a particular catapult
      
   3. On you best attempt, what was the largest wall that you softball would have cleared if the wall was at some location (say 10 meters from the catapult)
      
   4. How long did it take the softball to get to its maximum height?
      
   5. Given a range of 30 meters, how could you increase the time that a softball stays in the air? The judges will assign a score of 0 to 15 points for this work.

   Winner:
   The team with the highest total score will be the winner of the contest.

Mousetrap Car Race
Objective:
Each team is to produce one vehicle powered by a mousetrap. The vehicle should travel a distance of 10 meters in the shortest possible time.
Apparatus:
Each team is responsible for designing and building one mousetrap-powered vehicle prior to the competition. UNT will provide the timing system.
Regulations:

1. A mousetrap spring is to provide the sole source of power for the vehicle. NO other stored energy supplies -- including gravitational
   potential energy -- may be released by the spring.
2. The trap used to power the vehicle must be sold commercially as a mousetrap. As such, the trap spring should consist of a steel wire
   nominally 1.3mm in diameter wound into a coil nominally 7mm in diameter with approximately 20 turns. Rat traps, or any other traps with springs differing significantly from that just described, will be disqualified.
3. The mousetrap spring and the portion of the trap board to which the spring is attached may not be altered in any way. The trap restraining arm and other portions of the board may be modified. In no case should the spring move through an angle of more than 180 degrees.
4. The mousetrap must be contained in the vehicle and must propel the vehicle by means of a wheel or wheels in contact with the ground. A launcher of device that pushes the vehicle from a stationary object is prohibited.
5. One wheel of the vehicle must remain in contact with the ground at all times.
6. The vehicle must remain as a single unit at all times.
7. The vehicle must have a mass of at least 0.5kg.
8. The vehicle must be started from a standstill by releasing the mousetrap spring in a manner that imparts no additional energy to the vehicle; i.e., the vehicle may not be given a push start.
9. The race course will consist of a hard, smooth, level surface with lanes for individual vehicles each 10 meters long and 2 meters wide. The time interval required for each vehicle to cover the 10 meters will be measured from the time the leading edge of the vehicle's front wheel breaks the plane of the stating ling to the time the leading edge of the same wheel breaks the plane of the finish line. If the vehicle does not travel the entire 10 meters, then the distance traveled from the start will be used to determine the vehicle's score. If the vehicle leaves the lane from either side, it will be considered stopped when it breaks the plane of the lane boundary.

Scoring:

1. 20 points will be awarded to each team that shows up with a viable vehicle.
2. 40 points will be awarded to each vehicle completing the 10 meter distance. If a vehicle completes a fraction of the full distance, the
   corresponding fraction of 40 points will be awarded.
3. Vehicles completing the 10 meter distance will be awarded up to 40 additional points based on the time required to complete the distance. The overall fastest time of the day for the entire field of entries will be divided by an individual vehicle's finish time to determine the fraction of 40 points awarded to that vehicle. The standing overall fastest time will be posted for reference while the competition is in progress.
4. Each vehicle will be allowed to complete two runs. The vehicle's best time/distance will then be used to determine its score.
5. The top scoring 10% of competing vehicles will participate in a final heat, from which the winners will be decided.

Spontaneous Event
Objective:
To solve, as a team, some simple problem with a limited set of resources.
Procedure:
The team will first be given a short lecture on some basic physical principle. Each team will then be isolated in a room with a single judge. The judge will present the team with a task relating to the lecture and a set of materials with which to perform this task. A time limit will be set, and the method of solution will be as important as the solution itself.
Other:
No further information will be provided on this event, and no questions may be asked until the event is completed.

Egg Drop
Objective:
To design a container that will protect a Grade A Medium egg from a fall of about 20 meters (5 stories) onto a concrete surface.
Apparatus:
Each team will construct one container. Each team will be responsible for the secrecy of their design. We will provide the eggs and they will
be raw.
Regulations:
The container must be able to fit inside a box of dimensions 40cmX40cmX40cm. The container may be constructed of any kind of material. The container must land within a 1 square meter area; the container will be dropped from a point directly above the center of the square meter landing area.
Procedure:
The container will be dropped from a hinged board, extending from a balcony over a concrete surface. The container does not have to survive the fall, but he egg must; a cracked of broken egg will disqualify the entry. The egg will be inspected by the judge within one minute of the drop. Only one drop will be made for each team's device.
Scoring:
Scoring will be based on the following equation:
score = mass + 10 X (time1 - time2)
where mass = mass of the egg container in grams (not including the egg),
time1 = time in seconds from release of the device until its impact,
time2 = sqr(2h/g) = time for an object to free fall when dropped from a height h under a gravitational acceleration g.
The device with the lowest score is the winner.

Fermi Questions
Objective:
To estimate the answers to order of magnitude questions
Apparatus:
Entire team, one pencil
Procedure:
The team members will work together to solve order of magnitude problems. All answers should be given in powers of ten. Teams have twenty minutes to complete the test.
Scoring:
Scoring is based upon the amount of error from accepted answers in powers of ten. Answers must be rounded to the nearest power of ten, so any mantissa greater than or equal to 5 forces an increase by one of the exponent. (e.g. 3 X 10^15 becomes 10^15, whereas 5 X 10^15 becomes 10^16)
Questions are scored as follows:
5 points for the correct exponent;
4 points for the exponent being within 1 (plus OR minus 1) of the
correct exponent;
3 points for the exponent being within 2;
2 points for the exponent being within 3;
1 point for being within 4;
0 points for the exponent being > 4 or <-4 of the correct exponent.
Examples:
What is the speed of light in centimeters per second?
(3 x 10^8 m/s)(100 cm/m) = 3 x 10^10 cm/s
An answer of 10^10 would receive 5 points;
an answer of 10^9 or 10^11 would receive 4 points;
an answer of 10^8 or 10^12 would receive 3 points;
an answer of 10^7 or 10^13 would receive 2 points;
an answer of 10^6 or 10^14 would receive 1 point.
Some other, more representative questions:
How many molecules of air are in your lungs right now that were in Julius Caesar's last breath?
How many cans of soda would it take to fill up an Olympic size swimming pool?

Electromagnet
Objective:
To build an electromagnet which will hold the greatest weight possible.
Apparatus:
The team is to supply a fully self-contained electromagnet. The device is not to exceed a height, width and length of 10cm, 15cm and 15cm, respectively. In addition, the width and length must be large enough to support the device, without any outside influence, across the 5cm X 5cm opening in the test stand. The electromagnet must be able to stand alone on a flat surface. The active region to the device is defined as the area to which the weight hanger will be attached. The active region must be flat and parallel to the stand surface. Additionally, the active region must be larger than a circle of radius 2cm. The device must be designed such that once on the test stand, the active region must be accessible from below. The device must hold a minimum of 250g to qualify. The power source, test stand, and weighing mechanism will be supplied by us.
Power Supply:
We will provide a 300 watt dc power source, with a maximum current rating of 15A and maximum voltage rating of 20V. The electromagnet must have 2 leads, accessible from above, to which the power source can be attached by means of 2 alligator clips.
Procedure:
The weight of the electromagnet will be recorded. One team member will then position the device on the test stand. The judge will attach the power supply, power up the magnet, then attach the weighing mechanism. Weight will be added at a constant rate until the magnet can no longer support the weight. The weight at this point will be recorded. (See Figure 2)
Scoring:
The score for each magnet is determined by the following formula:
(mass supported/mass of magnet)(100/best ratio)
where mass supported = maximum mass held by the device; best ratio = (mass supported/mass of magnet) of the best magnet; i.e., the largest ratio of all entries.

Bridge Build
Objective:
To design and construct a bridge that will support the greatest weight possible.
Apparatus:
Each team will supply one bridge composed only of paper and glue. The testing apparatus will be supplied by us.
Regulations:
The bridge must be free standing (with and without a load) with the highest point on the bridge being the roadbed, which must span the length of the bridge. The bridge must fit within the following dimensional ranges:

In addition, a 7cm x 7cm x7cm cube must be able to pass freely beneath the bridge from its lowest point up. The paper used for construction must be standard 8.5 x 11 inch notebook paper. No lamination is allowed. (Lamination is defined here as a build up of five or more consecutive layers of paper in direct contact or separated by only glue. Not - paper logs of more than four layers fall into this category.)
Procedure:
The weight of the bridge will be recorded. The bridge will then be placed upon a testing stand which will consist of two surfaces, level with respect to each other and separated by 20cm. A bar will be placed across the roadbed (perpendicular to the bridge's length) at the weakest looking point of the bridge (a bridge being no better that its weakest point) and the weight adding mechanism suspended from this bar. Weight will be added at a slow, steady rate until the bridge collapses or sags to 90% of its original height. At this point, the total weight suspended by the bridge will be recorded.
Scoring:
The score for the bridge build event is determined by the following formula:
score = (mass supported/mass of bridge)(100/best ratio)
where mass supported = maximum weight held by the bridge and best ratio = (mass supported/mass of bridge) of the best bridge; i.e., the largest ratio of all the entries.

Quiz Show
Objective:
To get correct answers to a 100 question quiz in a 30 minute time period.
Apparatus:
The entire team, one pencil.
Procedure:
The team members will work collectively to complete a 100 questions quiz in a 30 minute time period. The quiz will cover basic physics principles such as Newton's Laws, physics personalities, gravitation, optics, etc.
Scoring:
The team will receive a point for each correct answer. The number of correct answers is the team's final score for the event.

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