Physics midterm question: comparing relative amounts of energy changes

Physics 205A Midterm 2, fall semester 2019
Cuesta College, San Luis Obispo, CA

A 2.0 kg crate is attached to a block (of unknown mass) by use of an ideal rope and pulley. Starting from rest, the crate slides to the right while the block descends downwards, both with increasing speed. Ignore friction and drag. Determine which of these two energy forms undergoes a larger amount of change (increase or decrease) for this process, or if there is a tie:

translational kinetic energy of the crate;
gravitational potential energy of the block.

Explain your reasoning using the properties of energy forms, and conservation of energy.

[*] youtu.be/CgNlPOMOps0.

Solution and grading rubric:

• p:
  Correct. Applies energy forms and conservation concepts with:
  1. both the crate and the box are speeding up, such that their (same) final speed is faster than their initial speed (zero), making both their translational kinetic energy terms increase; and
  2. the box is going downwards, such that the final height is lower than the initial height, making its gravitational potential energy decrease; and
  3. sets up a transfer-balance energy conservation equation with the sum of the changes in translational kinetic energy of the crate, translational kinetic energy of the box, and gravitational potential energy of the box set to zero (as no energy is lost to non-conservative work); then
  4. since the decrease in gravitational potential energy of the box is "feeding" the increase in the translational kinetic energies of both the crate and the box; the gravitational potential energy of the box must undergo a larger change than the translational kinetic energy of the crate.
• 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. Correctly determines that no energy is lost to non-conservative work, but discusses how the decrease in gravitational potential energy of the block is transferred solely to the increase in translational kinetic energy of the crate (concluding that there is a tie in the amount of change of these two energy forms), while neglecting the increase in translational kinetic energy of the block.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at using properties of forces, work, energy forms and (non-)conservation of energy.
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach other than using properties of forces, work, energy forms and (non-)conservation of energy.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm02sQm5
p: 5 students
r: 1 student
t: 35 students
v: 9 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 1478):