Physics midterm question: Roman catapulta replica

Physics 205A Midterm 2, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 6.87

"Huge Roman Catapulta—'Tod's Stuff' was Head of Engineering"
Tod Todeschini
youtu.be/CgNlPOMOps0

A replica of a Roman catapulta was constructed for a TV show[*], using stored elastic potential energy to launch projectiles. From when the projectile is initially stationary to its highest point in its trajectory (where its velocity is momentarily horizontal), discuss why the change in elastic potential energy of the catapulta is (a) larger than the change in gravitational potential energy and also (b) larger than the change in translational kinetic energy of the projectile. Ignore friction/drag. Explain your reasoning using the properties of energy forms and energy conservation.

[*] youtu.be/CgNlPOMOps0.

Solution and grading rubric:

• p:
  Correct. Discusses/demonstrates that from start-to-finish elastic potential energy decreases, as the catapulta transfers this energy to the both the projectile's translational kinetic energy (as it is moving (horizontally) at the highest point in its trajectory) and the projectile's gravitational potential energy (as it is higher in elevation than when it started), thus the decrease in elastic potential energy is equal to the increase in translational kinetic energy and increase in gravitational potential energy, and thus must have a greater change than either one individually.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. At least understands that elastic potential energy is transferred to translational kinetic energy (in order to move the initially stationary projectile), and that elastic potential energy is also transferred to gravitational potential energy (as the projectile is higher than its starting point), but does not specifically show that these two energy increases together total the decrease in elastic potential energy, such that the change in elastic potential energy is greater than either individual energy change.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach other than that of applying energy conservation.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm02veR1
p: 25 students
r: 5 students
t: 13 students
v: 22 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 5425):