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Chapter 13: Q20P (page 380)

Mile-high building.In 1956, Frank Lloyd Wright proposed the construction of a mile-high building in Chicago. Suppose the building had been constructed. Ignoring Earth鈥檚 rotation, find the change in your weight if you were to ride an elevator from the street level, where you weigh600N, to the top of the building.

Short Answer

Expert verified

Change in weight from bottom to top of the building is-0.303N

Step by step solution

01

The given data

Weight at street level isW=600N (ignoring Earth鈥檚 rotation)

02

Understanding the concept of Gravitational acceleration

We use the concept of gravitational acceleration to find the change in weight of the person from the bottom to the top of the building. We can differentiate the equation to find the change in the acceleration. Using the change in acceleration, we can find a weight change.

Formula:

Gravitational acceleration,ag=GMr2 (i)

03

Calculation of change in weight from top to bottom

Differentiating acceleration of equation (i), we get

dag=-2GMer3dr

So the change in weight is,

Wtop-Wbottom鈮�m(dag)

We know,

Wbottom=GMemR2

We get,

mdag=-2GmMeR3dr=-2WbottomdrR

Putting the values we get,

mdag=-2(600)(1.61脳103)6.37脳106=-0.303N

The weight change is-0.303N

Negative sign indicates that decrease in weight.

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