Solving the Elevator Problem: Weight Measurement

[logan3]

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?

 

[A.T.]

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).

 

[TumblingDice]

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.

 

[CWatters]

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.

 

[athosanian]

of course, you should choose B.

 

[Chestermiller]

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.