Question

You've always wondered about the acceleration of the elevators in the 101 story-tall Empire State Building. One day, while visiting New York, you take your bathroom scale into the elevator and stand on them. The scales read 130 lb as the door closes. The reading varies between 100 lb and 150 lb as the elevator travels 101 floors.

Part A

What is the magnitude of the acceleration as the elevator starts upward?

Express your answer to two significant figures and include the appropriate units.

a

a

=

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Part B

What is the magnitude of the acceleration as the elevator brakes to a stop?

Express your answer to two significant figures and include the appropriate units.

Answer 1

1.

Using Force balance on bathroom scale in elevator, when elevator is going in upward direction:

F_net = W_app - W

From newton's 2nd law: F_net = m*a

W_app = apparent weight = reading on scale = 150 lb (since given that scale varies between 100 and 150 lb, so when accelerating upward then apparent weight will be higher)

W = Weight on stationary scale = 130 lb

So,

m*a = W_app - W

divide by 'W'

m*a/W = W_app/W - 1

Since W = m*g, So m/W = (1/g)

a/g = W_app/W - 1

a = g*(W_app/W - 1)

Using given values:

a = 9.81*(150/130 - 1)

a = 1.5 m/sec^2 = acceleration of elevator when moving upward

Part B.

When elevator is braking, then W_app = 100 lb, So

a = 9.81*(100/130 - 1)

a = -2.3 m/sec^2

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