How Does a Weighing Machine Measure True Weight?

[Ashu2912]

My book says that a weighing machine measures the normal reaction to us from the surface we are standing on... So, I basically have 2 doubts here:
(1) In Resnick, Halliday and Walker 6th edition (chapter on Laws of Motion), weight is defined as the magnitude of the force required to body a body from falling freely... So, my question is, does the weight, as per the above definition, be same in all cases? If no, does the weighing machine actually measure our weight as per the situation? Does the weighing machine "weigh" only in case the object is not accelerating in the vertical direction?
(2) Since the weighing machine measures the normal reaction, how does it actually work?

 

[sophiecentaur]

A 'weighing machine' is just a force meter (a spring and a scale to measure its extension). it just measures the downwards force (or the reaction force). To get the 'right answer' the weighing machine must not be accelerating upwards or downwards. Going up or down at fixed speed in a lift won't affect the reading.

 

[Filip Larsen]

So, my question is, does the weight, as per the above definition, be same in all cases? If no, does the weighing machine actually measure our weight as per the situation? Does the weighing machine "weigh" only in case the object is not accelerating in the vertical direction?

As a weighting machine measures the force by which an object pushes down on it, both the weight and the object must be non-accelerating relative to the surface of the Earth for the measurement to be "valid". And even then, the actual value measured may vary depending on your geographic latitude, height above sea level, and even air pressure for very light objects.

Since the weighing machine measures the normal reaction, how does it actually work?

Mechanical weights usually work by compression of a spring, where the compressed distance via some levers are translated to a dial calibrated to show weight.An electro-mechanical weight would instead use a piezoelectric sensor [1] or a strain gauge [2] to measure the weight which can be converted to an analogue or digital readout.

[1] http://en.wikipedia.org/wiki/Piezoelectric_sensor
[2] http://en.wikipedia.org/wiki/Strain_gauge

 

[EinsteinKillr]

A weighing machine is measuring the normal force equal and opposite the total force experienced by the object being weighed at the face where the machine and the object meet. Even thought the object may not be moving, it is still experiencing an accelerating force equal to to its mass times gravity. In SI units we call this Newtons ( 1 N = 1 kg * 9.8 m/s^2).

If a weighing machine were to measure the force experienced by a mass at the Earth's surface, it would read substantially higher than if it were to measure the force experienced by the same mass at a much higher altitude where the magnitude of the gravitational force is much smaller.

In either case, the weighing machine does "stop" the object from continued movement, but then again, so does the surface of the Earth. This is due more to nuclear forces and friction than anything else, as gravity is much weaker than the other forces.

Also, try to consider what the weighing machine would read if the object was dropped from some distance. Gravity would accelerate the object, and upon initially meeting the surface of the weighing machine, would transmit its momentum to it, resulting in a "weight" that was much higher than the actual mass of the object itself. However, given a short period of time, the kinetic energy of the object would move towards zero, and the weighing machine would be exerting a force upwards equal to that of gravity in the downwards direction. The final number would be of course, the weight of the object, or more precisely, the measure of the force required to keep the object in gravitational equilibrium.

 

[Filip Larsen]

Even thought the object may not be moving, it is still experiencing an accelerating force equal to to its mass times gravity.

I think that statement could easily be misunderstood. An object at rest with respect to some inertial reference system is by definition not accelerating and the total (accelerating a.k.a inertial) force on it is thus zero. If the object is at rest in a gravity field there must obviously be some other (surface) force that counter the force of gravity so that the sum is zero. The statement makes sense if you replace "accelerating" with "gravity".