4.1.2.P21
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A passenger is standing on a scale in an elevator. The building has a height of 500 feet, the passenger has a mass of 80 kg, and the scale has a mass of 7 kg. The scale sits on the floor of the elevator. (It is an Otis elevator, so we will label it as "O" so as not to confuse its forces with those caused by the earth.) You may take g = 10 N/kg. For doing this problem it might be useful to start by drawing free-body diagrams for the passenger and the scale.
Consider the vertical forces acting on the passenger and the scale
- WE→P: The force of the earth pulling down on the passenger (weight)
- WE→S: The force of the earth pulling down on the scale (weight)
- NP→S: The force of the passenger pushing down on the scale (normal)
- NS→P: The force of the scale pushing up on the passenger (normal)
- NO→S: The force of the elevator pushing up on the scale (normal).
- NO→P: The force of the elevator pushing up on the passenger (normal).
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 Source: Understanding Physics |
(a) Which of these forces affect the motion of the passenger?
(b) Which of these forces affect the motion of the scale?
(c) While the scale is sitting at rest on the 33rd floor, what can you say about the forces acting
- on the passenger?
- on the scale?
(d) The elevator now begins to descend. Starting from rest, it takes the elevator 6 seconds to get up to its downward speed of 12 m/s. Assuming that it is accelerating downward at a uniform rate during these 6 seconds, which of the forces in your diagram for (a) will change? For each force that changes, specify whether it will become bigger or smaller.
(e) While it is accelerating downward, which of the forces in your diagrams have the same magnitude? For each equality you claim, explain what foothold principle makes you think that they are equal.
(f) While it is accelerating downward, what does the scale read?
Joe Redish 9/17/15
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