Trebuchet Scoring Rubric

Name(s): ______

Category

/

Description

/ Data / Points Assigned / Points Awarded
Prototype #1 / due on Feb 26, on time, Can throw at least 0.25 m / 10 max
Prototype #2 / Due on Mar 1, On-time, functional, addresses issues from first. / 10 max
Inspection
Due: 3/8/10
Date: ______/ All points will be given in full if met completely. If not met, expect disqualification from competition or scoring after the lowest score of all competitors who did meet the qualifications in full. / On-time / 5 points off/day late
Follows directions given (or approved alternative) / 20 max.
Functional (throws at least 1 meter) / 20 max.
Longest Throw / The trebuchet that achieves the longest throw will receive max. points. / Distance of throw 1
Distance of throw 2
Distance of throw 3
Percentage of your best relative to longest
Points awarded (% times 10)
Analysis / Complete attached page, showing all work. / 25 points
Diagram or photo / Uses a ruler, prints neatly, labels all parts with names and sizes, etc. Label the throwing arm, counterweight, pivot, projectile location, and launching pin. / 5 points
Total Score
Grade


Analysis of the Trebuchet

from http://www.algobeautytreb.com/trebmath35.pdf

Fig. 1 The geometry of the trebuchet, showing the three angles taken as the independent variables, in a configuration at the start of the movement.

Fig. 2. The black box trebuchet with the range and initial conditions shown.

Using Figures 1 and 2 as guides, provide the data that corresponds to the symbols listed below.

NOTE: The position of fulcrum is considered to be x = 0, y = 0. All measurements are made relative to this point, with x being horizontal distance and y being vertical distance.

·  Position of top of lever when in loaded position, x1 = ______y1 = ______

·  Position of bottom of lever when in loaded position, x2 = ______y2 = ______

·  Position of projectile when in loaded position, x3 = ______y3 = ______

·  Position of counterweight when in loaded position, x4 = ______y4 = ______

·  Total distance that counterweight moves, h = ______

·  Length of counterweight arm, l1 = ______

·  Length of Projectile arm, l2 = ______

·  Mass of lever beam, mb = ______

·  Mass of counterweight, m1 = ______

·  Mass of projectile, m2 = ______

·  Angle between lever arm and the vertical, at the top of the lever, φ = ______

·  Angle between lever arm and the horizontal, at the bottom of the lever, ψ = ______

·  Height of the projectile from the ground when launched, y5 = ______

·  Angle of the launched projectile from the horizontal, a = ______

·  Measured Range of the projectile, R = ______

Calculations:

1.  Calculate the initial velocity of the projectile using the techniques learned in lab: Target Practice. Use the height y5 to find the time to the floor and the range R as the x-distance. A shortcut equation that you can use is .

2.  Calculate the kinetic energy in the projectile at the start of the trajectory as .

3.  Verify the distance, h, that the counterweight can fall, using h = l1(1 - cos(q)) = l1(1 + sin(y)).

4.  Calculate the potential energy of the counterweight mass m1 at a height h as.

5.  Calculate the maximum possible range using . (This equation is a combination of step 1, 2, and 3.)

6.  Calculate the percent difference between the max. range and your actual range.

7.  Use the max. range calculated in step 5 and find the initial velocity as discussed in step 1.

8.  Calculate the percent difference between the actual vo in step 1 and the ideal vo from step 7.