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Problem 4.8: Take a ride in an elevator
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A 50-kg box is riding in an elevator that accelerates upward or downward at a constant rate (position is given in meters and time is given in seconds). The box rests on a digital scale that records its apparent weight in newtons. The green arrow represents the instantaneous velocity of the elevator and its contents. Adjust the value of the acceleration (-9.8 m/s2 ≤ a ≤ 9.8 m/s2) and see how it affects the apparent weight. Restart.
- What type of force is recorded on the scale?
- Draw a free-body diagram for the box when its acceleration is 4.9 m/s2, 0 m/s2, and -4.9 m/s2.
- Write a formula for the scale reading as a function of the acceleration of the elevator, the mass of the box, and g.
- Determine the value of the elevator's acceleration that would make the force that the scale exerts on the box vanish In other words, how can the box become apparently "weightless?"
Script authored by Steve Mellema, Chuck Niederriter, and modified by Mario Belloni.
Problem authored by Mario Belloni.