20161015

Physics midterm question: trucks with different loads driving around circular turn

Physics 205A Midterm 1, fall semester 2016
Cuesta College, San Luis Obispo, CA

A truck drives at a constant speed at the top of a hill with a circular radius, then the truck drives at the same constant speed at the bottom of a dip with the same circular radius. In both cases the truck remains in contact with the road. Discuss why the normal force magnitude of the hill on the truck is less than the normal force magnitude of the dip on the truck. Explain your reasoning by using free-body diagram(s), the properties of forces and Newton's laws.

Solution and grading rubric:
  • p:
    Correct. Complete free-body diagram(s), and discusses/demonstrates:
    1. Newton's first law applies along the vertical direction, as there is no vertical motion, such that the magnitude of the upwards normal force of the road on the truck must equal the magnitude of the downwards weight force of Earth on the truck:

      N = mg;

    2. Newton's second law for uniform circular motion applies along the horizontal direction:

      ΣF = mv2/r,

      where the (maximum) static friction force fs = μsN pointing to the right (in the direction opposite attempted slipping to the left) provides the net force that points in towards the center of the circular motion:

      μsN = mv2/r;

    3. substituting N = mg into the above relation results in:

      μsmg = mv2/r,

      which means that the mass of the truck (whether carrying a light load or a heavy load) cancels out, and thus is not a factor in determining the maximum speed v that the truck would make around this radius r turn in order not to skid.
  • r:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Two of the three points (1)-(3) correct/complete.
  • t:
    Nearly correct, but argument has conceptual errors, or is incomplete.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some substantive attempt at applying Newton's laws to free-body diagram(s).
  • x:
    Implementation of ideas, but credit given for effort rather than merit. No systematic application of Newton's laws to the forces on free-body diagram(s).
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm01br1Q
p: 6 students
r: 9 students
t: 16 students
v: 11 students
x: 15 students
y: 0 students
z: 0 students

A sample "p" response (from student 2127):

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