Force Analysis of an Elevator Moving Upward

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An elevator moving upward experiences two forces: tension in the cable and gravitational force. When accelerating upward, tension (T) exceeds weight (w), while at constant velocity, T equals w. If the elevator accelerates downward, weight becomes greater than tension. For a 1,500 kg elevator accelerating upward at 2.5 m/s², tension can be calculated and should align with the initial upward acceleration scenario. Similarly, tension values for constant velocity and downward acceleration scenarios must be consistent with their respective conditions.
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(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)?
 
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