Question

E. Suppose you are standing on the scale in the elevator and the elevator is accelerating downward with
an acceleration smaller than 9.8 m/s2

i. Draw free-body diagrams of yourself, the scale, and the floor of the elevator where it interacts
with the scale.

ii. How must the magnitude of the force exerted by the scale on you compare with your own
weight?

iii. How must the reading on the scale compare with the reading you make when the elevator is
standing still or moving at uniform velocity?

iv. Is your conclusion about the size of the upward force exerted on you by the elevator
consistent with the sensation your experience during the short interval when an elevator
accelerates downward? Explain.

v. How must the total upward force exerted by the cables on the elevator compare with the total
weight of the elevator and its contents? Explain.

vi. What happens to the magnitude of the reading on the scale and the total upward pull of the
cables as the acceleration is made larger and larger? Explain.

E. Suppose you are standing on the scale in the elevator and the elevator is accelerating downward with an acceleration smaller than 9.8 m/s?. i. Draw free-body diagrams of yourself, the scale, and the floor of the elevator where it interacts with the scale. ii. How must the magnitude of the force exerted by the scale on you compare with your own weight? iii. How must the reading on the scale compare with the reading you make when the elevator is standing still or moving at uniform velocity? iv. Is your conclusion about the size of the upward force exerted on you by the elevator consistent with the sensation your experience during the short interval when an elevator accelerates downward? Explain.

Answer 1

(1)

Free body diagram of the person where N ý the normal reaction excersed by the scale to the person Ma is the weight of the person free body diagram of the scale ANI where N ý the normal reaction exerted by the floor on the scale. N is the reaction force exerted by the persons on the scale w u the welght of the scale Free body diagram of the floor

(2)

As the elevator is moving downwards Using the free body diagram of the person - N - Ma where a is the acceleration of the elevator Mg - Ma=N NOM (g-a) . so the force exerted by the scale that the weight of the person is less

(3)

when the elevator is standing still its acceleration is gero. NE Mxo Mg -N = 0 N= Mg so the is equal force N exerted by the to the actual weight scale on the person of the person.

(4)

Yes, when the elevator accelerates downwards the persoo inside the elevator feels some less weight than his actual weight.

(5)

ум lef y be the tension is the cables of the elevator and Meg be the weight of the elevator. Let a be the ownward accelerations of the elevator then As the elevator accelerates downwards MEG - TA MER u. Ta MEG ~ Ma (where, he is the mass? [ of the elevator . The total upward force T o is the cables of the & elevator is less than its actual weight.

(6)

using the free sody diagram of the person downwards with acceleration a As the elevator is moving - M - N = Man a. N= Mg - Ma As the acceleration becomes larger and of the reading in the scale N goes on larger, magnitude decreasing Similarly using the free body diagram of the elevator 4T MEG - T = MER TE MEG - Mean As the acceleration a becomes larger and larger, magnitude of the upward force T in the cables goes on decreasing,