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You know your mass is 67 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 87 kg. What is the acceleration of the elevator?

Answer :

The bathroom scale reads a higher value because the elevator is accelerating upwards. By applying Newton's second law of motion and knowing the actual mass, we can determine the elevator's acceleration is approximately 2.93 m/s².

Understanding Elevator Acceleration and Scale Reading

When standing on a bathroom scale in an elevator, the reading can change if the elevator accelerates. If your mass is 67kg and the scale reads 87kg, this means there is a greater force acting on you than just your weight due to gravity. This happens because the elevator must be accelerating upwards.

To find the elevator's acceleration, use Newton's second law of motion, which states that Force is equal to mass times acceleration (F=ma). Your apparent weight (the scale reading) represents the force exerted by the scale, which is the result of the actual gravitational force plus the force due to the elevator's acceleration.

The increase in apparent weight is the result of the additional force, so:

  • Additional force = apparent weight - real weight
  • Additional force = (87kg - 67kg) × 9.8 m/s² = 20kg × 9.8 m/s² = 196 N

Apply Newton's second law to find acceleration:

  • Additional force = mass × elevator's acceleration
  • 196 N = 67kg × elevator's acceleration
  • Elevator's acceleration = 196 N / 67kg ≈ 2.93 m/s²

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