Physics midterm question: accelerating/decelerating upwards moving elevators

Physics 205A Midterm 1, fall semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 4.23(a)

Two elevators have the same mass of 800 kg, and both move upwards pulled by cables. Elevator 1 moves with an increasing upwards speed, while elevator 2 moves with an decreasing upwards speed. Discuss why the tension in the cable pulling elevator 1 is greater than the tension in the cable pulling elevator 2. Explain your reasoning by using the properties of forces and Newton's laws.

Solution and grading rubric:

• p:
  Correct. For both elevators, a cable exerts an upwards tension force, while Earth exerts a downwards weight force. The downwards weight force has the same magnitude ((800 kg)⋅(9.80 N/kg) = 7.8×10³ N) for both elevators. Discusses that the acceleration of elevator 1 must point upwards, and so must the net force on elevator 1, and thus the tension force on elevator 1 must be greater than the weight force of 7.8×10³ N; and the acceleration of elevator 2 must downwards, and so must the net force on elevator 2, and thus the tension force on elevator 2 must be less than the weight force of 7.8×10³ N.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. May have net forces pointing upwards for both elevators; weight force vectors drawn with different lengths for the elevators; tension force on elevator 2 more than the weight force (but less than the tension force on elevator 1), etc.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. At least some application of Newton's laws in relating direction net force with acceleration, and how two opposite forces combine to obtain a net force.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least some attempt at drawing a free-body diagram and discussing properties of forces.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Application of concepts other than those of forces and Newton's laws.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm01p0To
p: 11 students
r: 16 students
t: 13 students
v: 32 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 1216):