Physics midterm problem: pushing box up ramp

Physics 205A Midterm 1, Spring 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 to push a 40.0 kg box up a 18.0 degree ramp. The coefficient of kinetic friction between the box and the ramp is 0.290. With what magnitude force parallel to the ramp should the student push on the box so that it moves up the ramp at constant speed?

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 in both x- and y-directions to find normal force of ramp on box, and applied force on box (which is equal to w_x + f_k).
  
• r = 16/20:
  Nearly correct, but includes minor math errors. Typically uses N = w = m*g instead of N = w_y = m*g*cos(theta), otherwise methodical application of Newton's first law along x-direction; or sets F_app = f_k only, neglecting w_x component, but has N = w_y correct.
  
• 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 methodical application of Newton's first law. May have both of the two errors described in (r).
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Serious attempt at free-body diagram or 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 30880, 30881
p: 8 students
r: 8 students
t: 14 students
v: 14 students
x: 1 student
y: 1 student
z: 0 students

A sample "p" response (from student 1830):

A sample "r" response (from student 4444), where the x-component of weight is ignored:

Another sample "r" response (from student 2679), where the x-component of weight is included, but the normal force was set equal to the magnitude of weight, instead of its y-component:

A sample "t" response (from student 0406), including both errors described above from the previous sample "r" responses: