Physics midterm question: net force on car making a turn

Physics 205A Midterm 1, fall semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 5.38

A car makes a circular turn at constant speed along a dry, flat road, without skidding. The net force on the car is directed:
(A) up (in the +y direction).
(B) down (in the –y direction).
(C) in towards the center of the turn.
(D) out away from the center of the turn.
(E) (This quantity is zero, and thus has no direction.)

Correct answer (highlight to unhide): (C)

The car has two vertical forces acting on it:

Weight force of Earth on car (downwards, magnitude w = m·g).
Normal force of floor on car (upwards, magnitude N).

Because the car is stationary in the vertical direction, these two forces are equal in magnitude and opposite in direction, due to Newton's first law.

The car has only one horizontal force acting on it:

Static friction force of road on car (f_s, as it is not skidding)
      (into the center of the turn, opposing tendency to slide outwards).

Since the car is in uniform circular motion, Newton's second law is applicable here, such that the net force must point in towards the center of the turn. Thus the static friction force provides the requisite inwards net force on the car to maintain its uniform circular motion.

Sections 70854, 70855, 73320
Exam code: midterm01p0To
(A) : 5 students
(B) : 3 students
(C) : 53 students
(D) : 26 students
(E) : 4 students

Success level: 73%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.38