Physics midterm problem: SmartCar wet pavement turn

Physics 205A Midterm 1, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 5.19, Comprehensive Problem 5.75

"Tiny U circle in a smart car"
Guy Smith
youtu.be/eO4KiKAk7kE

A SmartCar Pure Coupe (mass of 900 kg[*]) can turn around in a circle with a minimum radius of 4.4 m[**]. If the coefficient of static friction between tires and a wet parking lot is 0.20[***], what is the maximum possible speed for this turn on a flat, wet parking lot, without skidding? Show your work and explain your reasoning using a free body diagram, and the properties of forces, Newton's laws, and uniform circular motion.

[*] "Turning circle = 28.7 ft; ECE weight without driver = 1,808 lbs," smartusa.com/models/pure-coupe/specifications.aspx.
[**] "The size of a [turning] circle is actually its diameter, not its radius," wki.pe/Turning_radius.
[***] engineeringtoolbox.com/friction-coefficients-d_778.html.

Solution and grading rubric:

• p:
  Correct. Draws free-body diagram to illustrate that the normal force upwards must have the same magnitude as the weight force downwards, due to Newton's first law, and that the static friction force points inwards to satisfy Newton's second law for uniform circular motion (or these may be implicit in setting up N = m·g and µ_s·N = mv²/r equations). Solves for v..
  
• r:
  Nearly correct, but includes minor math errors. Correct numerical result, but no free body diagram or clear use of Newton's first law and Newton's second law, or free body diagram may include (fictitious) centrifugal forces.
  
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors.
  
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some attempt at applying Newton's laws.
  
• x:
  Implementation of ideas, but credit given for effort rather than merit. Use of angular kinematic equations, etc.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: midterm01w4Sh
p: 18 students
r: 8 students
t: 4 students
v: 12 students
x: 10 students
y: 0 students
z: 1 student

A sample "p" response (from student 3389):