Solving the Elevator Problem: Weight Measurement

  • Thread starter logan3
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In summary, the person's weight and the upwards force on the person are both acting on the bathroom scale, but the upwards force is greater.
  • #1
logan3
83
2
A person who normally weighs 700 N is riding in an elevator that is moving upward but
slowing down at a steady rate. If this person is standing on a bathroom scale inside the elevator,
what would the scale read?

A) 700 N
B) less than 700 N
C) more than 700 N
D) It could be more or less than 700 N, depending on whether the magnitude of the
acceleration is greater than or less than 9.8 m/s2.
I don't understand how the forces work in this problem. Gravity points down and I make it be negative direction. Then an equal but opposite force points up. Then there is another acceleration going down since the elevator is slowing down. This make the total acceleration downwards even larger. So wouldn't the person weigh more, not less?
 
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  • #2
logan3 said:
So wouldn't the person weigh more, not less?
The weight of the person is always the same and pointing downwards. The scale shows the upwards contact force on the person. If the person accelerates downwards, the net force must be downwards, so the upwards force (scale) must be less than the downwards force (weight).
 
  • #3
logan3 said:
I don't understand how the forces work in this problem. Gravity points down and I make it be negative direction. Then an equal but opposite force points up. Then there is another acceleration going down since the elevator is slowing down. This make the total acceleration downwards even larger. So wouldn't the person weigh more, not less?
Bathroom scales are calibrated for the acceleration factor of Earth's gravity (32 ft/sec^2). When an elevator begins upwards acceleration, this acceleration is added to the acceleration component of Earth's gravity. That results in more force downwards from your inertial mass on the bathroom scale, and the scale indicates a greater value.

If the elevator reaches a steady velocity upward, gravity is now the only acceleration force and the bathroom scale will indicate the normal value for your weight.

Once the elevator begins 'braking', an acceleration component opposite to that of gravity is applied, which now subtracts from the acceleration force of gravity, reducing the net acceleration, and the bathroom scale indicates a lesser value than normal.
 
  • #4
Then there is another acceleration going down since the elevator is slowing down.

but is that acting on the person or the elevator? The scales are "squeezed" between the two.
 
  • #5
of course, you should choose B.
 
  • #6
Logan3,

Have you drawn a free body diagram of the person? What are the external forces acting on the person? Write down your equation for the force balance using Newton's second law.
 

Related to Solving the Elevator Problem: Weight Measurement

1. What is the elevator problem?

The elevator problem refers to the issue of accurately measuring the weight of passengers in an elevator in order to prevent overloading and ensure safe operation.

2. Why is weight measurement important in elevators?

Weight measurement is crucial in elevators because exceeding the weight limit can lead to malfunctions or accidents, potentially causing harm to passengers and damaging the elevator.

3. How is weight measured in elevators?

Weight is typically measured in elevators using a load sensor system, which can be either hydraulic or electrical. The system calculates the weight based on the amount of pressure or strain applied by the passengers in the elevator.

4. What are the factors that affect weight measurement in elevators?

There are several factors that can affect weight measurement in elevators, including the type and calibration of the load sensor system, the distribution of weight among passengers, and external factors such as temperature and humidity.

5. Can weight measurement in elevators be inaccurate?

Yes, weight measurement in elevators can be inaccurate due to a variety of factors such as sensor malfunction, uneven distribution of weight, or external influences. It is important for elevator companies to regularly calibrate and maintain their weight measurement systems to ensure accuracy.

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