Physics midterm question: truck driving over hill vs. through dip

Physics 205A Midterm 1, fall semester 2015
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 a free-body diagram, the properties of forces and Newton's laws.


Solution and grading rubric:

• p:
  Correct. Complete free-body diagrams, and discusses/demonstrates:
  1. Newton's second law for uniform circular motion applies, where the net force must point in towards the center of the circular motion, such that the net force on the truck on top of the hill points downwards, and the net force on the truck at the bottom of the dip points upwards;
  2. since the net force on the truck on top of the hill points downwards, the upwards normal force of the hill on the truck must have a smaller magnitude than the downwards weight force on the truck (N_hill < w); and since the net force on the truck at the bottom of the dip points upwards, the upwards normal force of the hill on the truck must have a greater magnitude than the downwards force on the truck (N_dip < w);
  as the weight force on the truck for either case remains the same (as it depends on the mass m and the gravitational constant g = 9.80 m/s²), then N_hill < w < N_dip, and thus N_hill < N_dip.
  (Although the magnitude of the net force is the same for both cases, this is not required in order to show that N_hill < N_dip.)
• 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 a free-body diagram.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No systematic application of Newton's laws to the forces on a free-body diagram.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm01j0r6
p: 19 students
r: 19 students
t: 6 students
v: 20 students
x: 11 students
y: 2 students
z: 1 student

A sample "p" response (from student 4815):
A sample "v" response (from student 2681), where the weight force on the truck is different in each case: