Physics midterm question: energy transfers for load-lowering winch

Physics 205A Midterm 2, fall semester 2017
Cuesta College, San Luis Obispo, CA

A load is attached to a cable that is wrapped around a cylindrical winch, which begins to rotate freely as the load drops downwards. From when the load is initially stationary to reaching a lower point (where it is moving with a downwards velocity), discuss why the change in gravitational potential energy of the load is:

1. greater than the change in the rotational kinetic energy of the winch; and
2. greater than the change in translational kinetic energy of the load.

Ignore friction/drag. Explain your reasoning using the properties of energy conservation.

Solution and grading rubric:

• p:
  Correct. Discusses/demonstrates that for this initial-to-final process:
  1. the gravitational potential energy of the load decreases (as its final height is lower than its initial height); and
  2. the rotational kinetic energy of the winch increases (as it has a final angular speed, compared to being initially at rest); and
  3. the translational kinetic energy of the load increases (as it has a final speed, compared to being initially at rest); and
  4. since there is no external work done on/by this system (as friction/drag is to be ignored); then
  5. from the transfer/balance energy conservation equation, the change in the gravitational potential energy of the load must be equal to the sum of the changes of the other two energy forms (rotational kinetic energy of the winch and translational kinetic energy of the load), and thus must have a greater change than either of those two forms.
• r:
  Nearly correct, but includes minor math errors.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least understands how all three energy forms are related to each other from the transfer/balance energy conservation equation.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some garbled attempt at applying energy conservation.
• 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
Exam code: midterm02bu2Z
p: 37 students
r: 3 students
t: 6 students
v: 4 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 7164):