Physics midterm problem: upward-sliding sponge

Physics 8A (currently Physics 208A) Midterm 2, spring semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Young and Freeman, University Physics, 11/e, Problem 3.63

A window washer pushes a sponge up a vertical window at constant speed by applying a force as shown at right. The sponge has a mass of 0.800 kg, and the coefficient of kinetic friction between the sponge and window is μ_k = 0.253. Determine the magnitude of the applied force, and the magnitude of the normal force exerted by the window on the sponge. Show your work and explain your reasoning using a free-body diagram, and the properties of forces, and Newton's laws.

Solution and grading rubric:

• p:
  Correct. Breaks up F_applied into x- and y-components. Applies Newton's first law in the x-direction, where:

  F_applied·cos(20.0°) = N.

  Then applies Newton's first law in the y-direction ("constant speed"), such that:

  F_applied·sin(20.0°) = m·g + μ_k·N.

  With two equations for two unknowns, solves for:

  F_applied = m·g/(sin(20.0°) - μ_k·cos(20°)) = 75.2 N,
  
  N = m·g·cos(20.0°)/(sin(20.0° - μ_k·cos(20.0°) = 70.6 N.

• r:
  Nearly correct, but includes minor math errors. And/or has correct numerical value for only one of the forces.
  
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Correctly identifies all forces acting on the sponge. At least methodically applies Newton's first law in the x- and y-directions, with F_applied broken up into x- and y-components.
  
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Typically omits f_k acting downwards, and/or demands N = m·g while applying Newton's laws.
  
• x:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
p: 6 students
r: 4 students
t: 7 students
v: 11 students
x: 10 students
y: 0 students
z: 0 students