An object of mass m is hanging by a string from the roof of an
elevator. We want to compare the tension in the string due
to the weight of the object under various conditions. Which
statements are true?
Choices: True, False.
A. If the elevator is moving upwards, and speeding up, the
tension in the string is equal to the object's weight
B. If the elevator is moving up at constant speed, the tension in the string is equal to the object's weight
C. If the elevator is moving downwards, and speeding up,
the tension in the string is less than the object's weight
D. If the elevator is moving downwards in free fall, the
tension in the string is equal to the object's weight
E. If the elevator is moving upwards, but slowing down,
the tension in the string is equal to the object's weight
I will be happy to critique your thinking.
A. False
B. True
C. True
D. False
E. False
Are my answers correct?
all correct.
Thanks
To answer the question and determine which statements are true, we need to consider the different forces acting on the object in each scenario.
A. If the elevator is moving upwards, and speeding up, the tension in the string is equal to the object's weight. (True)
In this case, the object is accelerating upwards, and therefore, there is an additional force acting on it. The tension in the string must be greater than the object's weight to provide the upward force necessary for the acceleration.
B. If the elevator is moving up at constant speed, the tension in the string is equal to the object's weight. (True)
When the elevator is moving up at a constant speed, there is no net force acting on the object. The tension in the string must be equal to the object's weight, ensuring equilibrium.
C. If the elevator is moving downwards, and speeding up, the tension in the string is less than the object's weight. (False)
When the elevator is moving downwards and accelerating, the tension in the string must be greater than the object's weight to provide the additional force required for the acceleration. So, this statement is false.
D. If the elevator is moving downwards in free fall, the tension in the string is equal to the object's weight. (True)
In a free fall, the object and the elevator are in a state of weightlessness. In this case, there is no tension in the string since the object is not being supported.
E. If the elevator is moving upwards but slowing down, the tension in the string is equal to the object's weight. (False)
When the elevator is moving upwards but slowing down, there is a deceleration acting on the object. The tension in the string must be greater than the object's weight to provide the necessary upward force to counteract the deceleration.
Based on the analysis above, the true statements are A, B, and D.