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Suppose an elevator in the Empire State Building weighs 1,700 pounds. Find the work required to raise the elevator from ground level to the 93rd story, which is 1,116 feet above ground level.

Answer :

Final answer:

The work required to raise an elevator from the ground level to the 93rd floor of the Empire State Building, 1116 feet above, is calculated as 5,663,221.8 Joules using the formulas for force due to gravity and work done.

Explanation:

The question involves calculating the work done in lifting an elevator from ground level to a specific height. Work done, in a physics context, is the product of the force applied and the distance over which the force is applied. Specifically, for an elevator being raised vertically, the work done is equivalent to the force of gravity acting on the elevator's mass over the vertical distance. The force of gravity can be calculated using the formula F = mg, where m is the mass and g is the acceleration due to gravity (9.8 m/s2). Since the mass provided is in kilograms and the height in feet, we'll first convert the height to meters (1 foot = 0.3048 meters).



To find the work, the formula W = Fd is used, where F is the force of gravity and d is the height in meters. Now, substituting the given values:

  • First, convert the height: 1116 feet x 0.3048 = 340.13 meters.
  • Calculate the force of gravity: F = 1700 kg x 9.8 m/s2 = 16660 N.
  • Calculate the work done: W = 16660 N x 340.13 m = 5,663,221.8 Joules.

The work required to raise the elevator to the 93rd floor is therefore 5,663,221.8 Joules.

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