Physics quiz question: upwards-accelerating elevator

Physics 205A Quiz 3, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Multiple Choice Questions 4.9, 4.10, 4.11, Problems 4.25, 4.26

A 400 kg elevator attached to a cable moves upwards, increasing its speed with an acceleration of magnitude 1.5 m/s2. The __________ on the elevator has the smallest magnitude.
(A) tension force of cable.
(B) weight force of Earth.
(C) net force.
(D) (More than one of the above choices.)
(E) (Not enough information is given.)

Correct answer (highlight to unhide): (C)

The tension force of the cable on the elevator is upwards, and the weight force (of Earth) on the elevator is downwards. These are the only two vertical forces on the elevator, and since the direction of the elevator's acceleration is upwards, then from Newton's second law these forces must sum to a net force that points upwards, and the tension force must be greater in magnitude than the weight force.

The magnitude of the net force is given by Newton's second law:

ΣFy = m·ay,

ΣFy = (400 kg)·(1.5 m/s2) = 600 N,

and is directed upwards. The weight force has a magnitude:

w = m·g = (400 kg)·(9.8 m/s2) = 3,900 N,

and is directed downwards. The magnitude of the tension force can then be solved for:

ΣFy = +T - w,

+600 N = T - 3,900 N,

4,500 N = T.

Thus the tension force has the greatest magnitude, followed by the weight of the elevator, and the net force on the elevator has the smallest magnitude.

Sections 70854, 70855
Exam code: quiz03sQr7
(A) : 3 students
(B) : 23 students
(C) : 27 students
(D) : 2 students
(E) : 0 students

Success level: 49%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.58

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