Question

A 84-kg man stands on a bathroom scale inside an elevator. the scale measures in units of newtons. (a) the elevator accelerates upward from rest at a rate of 1.20 m/s2 for 1.50 s. what does the scale read during this 1.50 s interval

Answer 1

Answer:

  94 kg

Explanation:

The mass registered by the scale is based on the assumption that the force applied is due entirely to gravity. If the force is greater, then the indicated mass will be greater.

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how many g's

As a fraction of the acceleration of gravity, the elevator's acceleration is ...

  (1.2 m/s²)/(9.8 m/s²) ≈ 6/49

net force

The force required to produce a given acceleration is found by the formula ...

  F = ma . . . . . . . force on mass m to produce acceleration 'a'

When the man is stationary on the scale, the upward force it supplies is balanced by the downward force on the man due to gravity. The force and the mass are proportional, and the constant of proportionality (the acceleration due to gravity) is used to calibrate the scale. More force is thus translated to a higher mass reading.

Since the man's net acceleration is upward at the rate of 6/49×g, the total force applied by the scale is (1 +6/49) = 55/49 times as great as when the man is stationary. This greater force gets translated to a greater mass reading.

The force is equivalent to what would be required to support a stationary man with a mass of ...

  (84 kg)(55/49) = 94 2/7 kg

The scale would read about 94 kg during the upward acceleration period.