20121013

Physics midterm question: free-body diagram of upside-down car at top of loop

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

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

Which free-body diagram (A)-(F) represents a car (upside-down) at the top of a vertical loop, traveling fast enough that it is still in contact with the loop? Clearly circle your answer below.


Correct answer (highlight to unhide): (A)

Assuming that the speed of the car is momentarily constant as it travels (upside-down) at the highest point of a vertical loop, then the net force must point in towards the center of the circle (downwards). This eliminates choices (D) and (F) (which both have a zero net force), and also eliminates choice (E) (which has an upwards net force, pointing out away from the center of the vertical circle). This leaves choices (A)-(C) as potentially correct free-body diagrams, as each of their net forces points downwards (in towards the center of the vertical circle).

The upside-down car has two vertical forces acting on it:
Weight force of loop on car (downwards, magnitude w = m·g).
Normal force of loop on car (downwards, magnitude N ≠ 0, as car is still in contact with the loop).
Since these two forces both point downwards, then the correct free-body diagram is (A), where the two downward forces of weight and normal force both contribute to the requisite downward net force. Response (B) would be possible only if the car momentarily loses contact with the loop; while response (C) is not possible for an upside-down car at the top of a vertical loop, as neither the weight force nor the normal force of the loop on the car can point upwards.

Sections 70854, 70855
Exam code: midterm01sWFf
(A) : 6 students
(B) : 1 student
(C) : 25 students
(D) : 3 students
(E) : 16 students
(F) : 6 students

Success level: 11%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.08

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