# Mass vs. weight on a spring-loaded bathroom scale

You stand on a spring-loaded bathroom scale in a bathroom. The scale "reads" your mass. What is the scale actually measuring?

Similarly, you stand on a spring-loaded bathroom scale in an elevator that is accelerating upward at 2.0 m/s^2. The scale "reads" your mass. What is the scale measuring?

A) Your mass B) Your weight C) The force of the scale pushing up on your feet D) The force of your feet pushing down on the scale

To me, C seems correct for both of them, but B also seems correct for the first part, as weight is equal to the force of the scale on your feet for that part. Can anyone corroborate or deny my assumptions?

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It is measuring the reaction force from gravity on your body. Actually it is measuring the deflection of a calibrated spring under the influence of the reaction force. – ja72 Sep 5 '12 at 16:11

## 2 Answers

What is the scale actually measuring?

The external force acting to extend or compress the spring.

Since this force is proportional to the mass of the object being weighed via $f=ma$, the mass can be inferred if the acceleration of gravity (or of gravity and the elevator) is known.

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You are right C is correct. Actually C and D are equivalent in magnitude and opposite in sign and cancel. For the static case B - Your weigh is just a different way of saying C. Weight being the force generated by your mass with g~=9.8 m/s^2.

In the elevator case the scale is measuring the force that your mass in the earths field is generating + the foce from the acceleration of the elevator.

Interestingly, the mass that acceleration works on and the mass that graviatiy works on need not be the same. But they are.

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