Physics midterm problem: constant speed block down ramp

Physics 205A Midterm 1, Fall Semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 4.112

[20 points.] A Physics 205A student wants a 20 kg box to slide with constant speed down a ramp that is inclined 10° from the horizontal. The coefficient of kinetic friction between the ramp and box is 0.40. What direction (up along the ramp, or down along the ramp) and magnitude force should the student exert on the box such that it slides down the ramp with constant speed? Assume that the box has already been unstuck. Show your work and explain your reasoning.

Solution and grading rubric:

• p = 20/20:
  Correct. Resolves weight into w_x and w_y components (parallel and perpendicular to ramp, respectively). Then applies Newton's first law along the (tilted) y-direction to find normal force of ramp on box, and thus f_k = mu_k*N (pointing up along the ramp). Since f_k up along the ramp is larger than w_x down along the ramp, F_applied needs to be the difference between their magnitudes f_k - w_x.
  
• r = 16/20:
  Nearly correct, but includes minor math errors. Typically uses N = w = m*g or N = w_y = m*g/cos(10 degrees) instead of N = w_y = m*g*cos(degrees); or sets F_app = f_k only, neglecting w_x component, otherwise methodical application of Newton's first law along y- and x- direciton. May also have sines and cosines switched, calculator was used in radians mode, or spurious force/component added back in.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Some attempt at resolving w into components on a substantive free-body diagram, and/or methodical application of Newton's first law along (tilted) y- and x- directions. May have two errors/omissions of those described in (r).
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Serious attempt at free-body diagram and application of Newton's laws.
  
• x = 4/20:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Sections 70854, 70855, 72177
p: 12 students
r: 14 students
t: 12 students
v: 26 students
x: 1 student
y: 0 students
z: 0 students

A sample of a "p" response (from student 1717):
Another sample of a "p" response (from student 7895):
A sample of an "r" response (from student 2022), where the x- and y- components of weight were switched: