What Is the Maximum Acceleration of an Empire State Building Elevator?

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SUMMARY

The maximum acceleration of the Empire State Building's elevator can be calculated using the net force equation, Fnet = N - Fg. In this scenario, the normal force (N) varies between 120 lbs (533.4 N) and 170 lbs (756 N) as the elevator ascends and descends. The maximum upward acceleration occurs when the scale reads 170 lbs, while the maximum downward acceleration occurs at 120 lbs. The correct application of Newton's second law, along with the conversion of weight from pounds to Newtons, is crucial for accurate calculations.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with force equations (Fnet = N - Fg)
  • Knowledge of unit conversion between pounds and Newtons
  • Basic algebra for solving equations
NEXT STEPS
  • Study the application of Newton's second law in various contexts
  • Learn about the dynamics of elevators and their safety mechanisms
  • Explore the principles of force and motion in real-world scenarios
  • Investigate the effects of acceleration on human perception in elevators
USEFUL FOR

Physics students, engineers, elevator design professionals, and anyone interested in the mechanics of vertical transportation systems.

pdonovan
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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 it. The scale reads 150 lbs as the door closes. The reading varies between 120 lbs and 170 lbs as the elevator travels 101 floors.

a.)What is the maximium acceleration upward?
b.)What is the maximium magnitude of the acceleration downward?


I used the formula Fnet = N - Fg and still cannot get the correct answer.
I currently have ma = N - mg where m = 77.11kg, N = 756N, and g = 9.8.
So, 77.11a = 756 - 77.11(9.8)

Where did I go wrong?
Thank you for any help!
 
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Well, you know what the Fnet is.

If your just standing on the ground not moving, it's just your weight (well, it's zero if you count the ground pushing back up on you).

Bottom line is the scale is going to show the net downward force you exert on it. So you may want to set it up
Fnet = m*a + Fweight
 
How can Fnet = ma + Fweight when Fnet = ma?
 

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