## 20121013

### Physics midterm question: stacked, dragged boxes

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

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 4.63

A rope pulls box 1, such that both box 1 and box 2 both move together to the right at constant speed. All surfaces are not frictionless. Discuss why the friction force of box 1 on box 2 is directed to the right. Explain your reasoning by using free body diagram(s), the properties of friction, forces, and Newton's laws.

Solution and grading rubric:
• p:
Correct. Discusses that the (static) friction force of box 1 on box 2 must point to the right either because of (a) Newton's first law, in order for box 2 to move at constant speed to the right, the leftwards kinetic friction force of the floor on box 2 must be countered by a rightwards static friction force of box 1 and box 2; or (b) Newton's third law, as the static friction force of box 2 on box 1 points to the left, opposing box 1 from sliding off of the top surface of box 2, then the static friction force of box 1 on box 2 must point to the right.
• 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 some application of Newton's laws in relating direction of static friction force of box 1 on box 2 with another horizontal force.
• v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least some application of drawing a free body diagram and discussing properties of forces.
• x:
Implementation/application of ideas, but credit given for effort rather than merit.
• y:
Irrelevant discussion/effectively blank.
• z:
Blank.
Sections 70854, 70855
Exam code: midterm01sWFf
p: 6 students
r: 19 students
t: 15 students
v: 16 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 8921), using Newton's first law:

Another sample "p" response (from student 8821), using Newton's third law:

Another sample "p" response (from student 6377), drawing free body diagrams for both boxes, and establishing both Newton's first and third laws for the horizontal forces on the boxes: