Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 4.25, 4.26
A 600 kg elevator attached to a cable moves downwards, decreasing its speed with an acceleration of magnitude 1.5 m/s2. The force with the smallest magnitude is the:
(A) net force on the elevator.
(B) tension force of cable on the elevator.
(C) weight of the elevator.
(D) (More than one of the above choices.)
(E) (Not enough information is given.)
Correct answer (highlight to unhide): (A)
The elevator has two vertical forces acting on it:
Weight force of Earth on elevator (downwards).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.
Tension force of cable on elevator (upwards).
The magnitude of the net force is given by Newton's second law:
ΣFy = m·ay = (600 kg)·(1.5 m/s2) = 900 N,
and is directed upwards. The weight force has a magnitude:
w = m·g = (600 kg)·(9.8 m/s2) = 5,900 N,
and is directed downwards. The magnitude of the tension force can then be solved for:
+|ΣFy| = +|T − |w|,
+900 N = |T| − 5,900 N,
6,800 N = |T|,
where the positive signs indicate forces directed upwards, and the negative sign indicates a force directed downwards. Thus the tension force has the greatest magnitude (6,800 N), followed by the weight of the elevator (5,900 N), and the net force on the elevator has the smallest magnitude (900 N).
Sections 70854, 70855, 73320
Exam code: quiz03eL3v
(A) : 37 students
(B) : 14 students
(C) : 17 students
(D) : 2 students
(E) : 0 students
Success level: 53%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.63
2 comments:
Why did you substitute Tension and Weight into newtons second law equation?
The sum of the forces acting on the elevator is the vector addition of the tension force (upwards) and the weight force (downwards).
From Newton's second law, the sum of the forces (net force) is equal to mass times acceleration.
So we equate the two expressions for the net force:
Net force = tension (upwards) and weight (downwards, this is where the negative sign will eventually come in),
Net force = mass times acceleration.
Then for this situation, mass times acceleration is equal to the vector addition of the tension (upwards) and weight (downwards) forces.
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