Force Analysis of an Elevator Moving Upward

[ahh86]

please help me...

(a) An elevator of mass m moving upward has two forces
acting on it: the upward force of tension in the cable and
the downward force due to gravity. When the elevator is
accelerating upward, which is greater, T or w? (b) When
the elevator is moving at a constant velocity upward,
which is greater, T or w? (c) When the elevator is moving
upward, but the acceleration is downward, which
is greater, T or w? (d) Let the elevator have a mass of
1 500 kg and an upward acceleration of 2.5 m/s2. Find T.
Is your answer consistent with the answer to part (a)? (e)
The elevator of part (d) now moves with a constant up-
ward velocity of 10 m/s. Find T. Is your answer consistent
with your answer to part (b)? (f) Having initially moved
upward with a constant velocity, the elevator begins to ac-
celerate downward at 1.50 m/s2. Find T. Is your answer
consistent with your answer to part (c)?

 

[zwtipp05]

https://www.physicsforums.com/showthread.php?t=94379

 

[quicknote]

I would like to clarify a few concepts before answering the questions. Firstly, the tension force in the cable is not always equal to the weight force due to gravity. The tension force is dependent on the acceleration of the elevator, whereas the weight force remains constant. Secondly, it is important to note that the direction of the elevator's acceleration and velocity may affect the direction of the tension force.

(a) When the elevator is accelerating upward, the tension force will be greater than the weight force due to gravity. This is because the elevator is moving in the same direction as the tension force, causing an increase in tension force to overcome the weight force.

(b) When the elevator is moving at a constant velocity upward, the tension force and weight force will be equal. This is because the elevator is not accelerating, so the tension force does not need to increase to overcome the weight force.

(c) When the elevator is moving upward but accelerating downward, the weight force will be greater than the tension force. This is because the elevator is moving in the opposite direction of the tension force, causing a decrease in tension force and an increase in weight force.

(d) Using the given values, we can calculate the tension force as follows:
T = m(a + g)
T = (1500 kg)(2.5 m/s^2 + 9.8 m/s^2)
T = 19,350 N
This answer is consistent with the answer in part (a), where the elevator was accelerating upward.

(e) Using the given values, we can calculate the tension force as follows:
T = mg
T = (1500 kg)(9.8 m/s^2)
T = 14,700 N
This answer is consistent with the answer in part (b), where the elevator was moving at a constant velocity upward.

(f) Using the given values, we can calculate the tension force as follows:
T = m(g - a)
T = (1500 kg)(9.8 m/s^2 - 1.5 m/s^2)
T = 12,300 N
This answer is consistent with the answer in part (c), where the elevator was accelerating downward.

In conclusion, the tension force in the cable is dependent on the acceleration and direction of motion of the elevator. When the elevator is accelerating upward, the tension force will be greater than the weight force. When the elevator is moving at a constant velocity, the tension force