Physics final exam problem: force applied to accelerating box

Physics 205A Final Exam, fall semester 2016
Cuesta College, San Luis Obispo, CA

A horizontal force of 4.0 N is applied to a 1.5 kg box sliding to the right along a floor as it speeds up with an acceleration of 0.51 m/s². Determine (a) the magnitude and direction of the kinetic friction force on the box; and (b) the kinetic friction coefficient µ_k for the box and the floor. Show your work and explain your reasoning using free-body diagrams, the properties of forces, and Newton's laws.

Solution and grading rubric:

• p:
  Correct. Draws a free-body diagram the box, and:
  1. applies Newton's first law to the vertical forces on the box, showing that the magnitudes of these forces are equal: weight (gravitational) force of Earth on the box (downwards), normal force of the floor on the box (upwards), (this does not have to explicitly shown if implied in step (4) below);
  2. applies Newton's second law to the horizontal motion of the box, such that the magnitude of the net force (which points to the right) is equal to the product of the mass and acceleration;
  3. applies Newton's second law to the horizontal forces on the box, showing that the magnitude of the net force is equal to the difference between the: applied force on the box (to the right), kinetic friction force of the floor on the box (to the left), and finds the direction and magnitude of the kinetic friction force;
  4. applies the definition of the kinetic friction force being the product of the coefficient µ_k and the normal force (which has a magnitude equal to the weight force) solve for the value of µ_k.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. At least recognizes that Newton's first law applies in the vertical direction, and Newton's second law applies in the horizontal direction.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some substantive attempt at applying properties of forces and Newton's laws to free-body diagrams; may not have explicitly noted which Newton's law applies to the horizontal motion of the box.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No systematic application of properties of forces and Newton's laws to the forces on free-body diagrams.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: finali0w4
p: 15 students
r: 1 student
t: 19 students
v: 9 students
x: 5 students
y: 0 students
z: 0 students

A sample "p" response (from student 1317):