Physics midterm problem: Swiffer® Sweeper force

Physics 205A Midterm 1, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 4.65


"Cleans more than us"
Christopher Heschong
flic.kr/p/7G7H4n

A child pushes along the handle of a Swiffer® Sweeper at an angle of 55° with respect to the vertical. If the mass of a dry Swiffer® Sweeper pad is 0.15 kg, and the coefficient of kinetic friction between the pad and the floor[*] is 0.17, determine the amount of force applied along the handle for a Swiffer® Sweeper pad to slide along the horizontal floor with constant speed. Show your work and explain your reasoning using a free-body diagram, and the properties of forces, and Newton's laws.

[*] flic.kr/p/dftcPA.

Solution and grading rubric:

• p:
  Correct. Draws free body diagram to illustrate that the normal force upwards must have the same magnitude as the y-component of the applied force plus the weight force downwards, due to Newton's first law; and that the x-component of the applied force must have the same magnitude as the static friction force points, also due to Newton's first law. Then expresses Newton's first law in the vertical (N = w + F_applied,x) and horizontal (F_applied,y = f_k) directions, and substitutes f_k = μ_k∙N to solve for the magnitude of the applied force.
• r:
  Nearly correct, but includes minor math errors.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Typically neglects y-component of applied force, such that the upwards normal force is set equal in magnitude to the downwards weight force. Then uses N = w = m∙g result to calculate kinetic friction force f_k = μ_k∙N = 0.25 N, and equates this f_k to the x-component of the applied force, using trigonometry to determine magnitude of applied force.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Free body diagram identifies most forces and their directions, with some attempt at applying Newton's laws.
• x:
  Implementation of ideas, but credit given for effort rather than merit. Garbled/incomplete free body diagram with little to no application of Newton's laws, etc.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm01sWFf
p: 1 student
r: 3 students
t: 30 students
v: 11 students
x: 12 students
y: 0 students
z: 0 students

A sample "p" response (from student 6377):
A sample "t" response (from student 2507), where the magnitude of the normal force is set equal to the weight of the pad: