What happens to the spring of a bathroom scale when a weight is placed on it?

Essie S.

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asked • 10/04/16

Hi, everyone. Im not sure what the answer is. Can you briefly explain ? I think it has something to do with weight force.

2 Answers By Expert Tutors

Scales, oddly enough, don't measure the force of gravity acting down on it. They measure the normal force pushing back up against whatever object is placed on it.

If you draw a mass on an inclined plane, you'll see that the gravitational force always points straight down with mg as its magnitude.

Normal force is perpendicular to the incline and has a magnitude of mg*cos(theta), with theta equaling whatever angle your incline is at.

If your angle is anything other than 0 degrees (i.e. horizontal to the surface) it will have profound effects on the magnitude of the normal force (which is what the scale is measuring). This is because

Say you weigh 120 pounds, and you weigh yourself on a scale tilted at an incline of 60 degrees. The force of gravity would still be 120 pounds downward, but the normal force that the scale is actually measuring would be:

The extreme of this case would be trying to stand on a scale upright at a 90 degree angle to the floor. As we know from trigonometry,

So the normal force in the instance would be

Thus your scale would be reading zero, which makes sense, because you wouldn't be physically capable of standing on it.

This is why your scale needs to be horizontal to the ground; strictly to make sure cos(theta) = 1, which only occurs at 0 degrees.

Adam V. answered • 10/04/16

Professional Software Engineer, over 10 years work experience!

It has to do with the direction of the downward force that registers as weight.

Weight = mass * gravity, and the force of gravity pulls straight down towards the center of the earth. That means that to measure the full force of gravity, the scale needs to be perpendicular to the force vector, which means it needs to be horizontal.

If the scale is tilted, it will only be measuring a portion of the straight down force vector, which will result in an incorrect weight being displayed.

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Mechanism to measure force based on the extension of a spring

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A spring scale

A spring scale, spring balance or newton meter is a type of mechanical force gauge or weighing scale. It consists of a spring fixed at one end with a hook to attach an object at the other. It works in accordance with Hooke's Law, which states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance. Therefore, the scale markings on the spring balance are equally spaced.

A spring balance can be calibrated for the accurate measurement of mass in the location in which they are used, but many spring balances are marked right on their face "Not Legal for Trade" or words of similar import due to the approximate nature of the theory used to mark the scale. Also, the spring in the scale can permanently stretch with repeated use.

A spring scale will only read correctly in a frame of reference where the acceleration in the spring axis is constant (such as on earth, where the acceleration is due to gravity). This can be shown by taking a spring scale into an elevator, where the weight measured will change as the elevator moves up and down changing velocities.

If two or more spring balances are hung one below the other in series, each of the scales will read approximately the same, the full weight of the body hung on the lower scale. The scale on top would read slightly heavier due to also supporting the weight of the lower scale itself.

Spring balances come in different sizes. Generally, small scales that measure newtons will have a less firm spring (one with a smaller spring constant) than larger ones that measure tens, hundreds or thousands of newtons or even more depending on the scale of newtons used. The largest spring scale ranged in measurement from 5000–8000 newtons.

A spring balance may be labeled in both units of force (poundals, Newtons) and mass (pounds, kilograms/grams). Strictly speaking, only the force values are correctly labeled. In order to infer that the labeled mass values are correct, an object must be hung from the spring balance at rest in an inertial reference frame, interacting with no other objects but the scale itself.

Uses

Example of spiral balancer for Sash window

Main uses of spring balances are to weigh heavy loads such as trucks, storage silos, and material carried on a conveyor belt. They are also common in science education as basic accelerators. They are used when the accuracy afforded by other types of scales can be sacrificed for simplicity, cheapness, and robustness.

A spring balance measures the weight of an object by opposing the force of gravity acting with the force of an extended spring.

History

The first spring balance in Britain was made around 1770 by Richard Salter of Bilston, near Wolverhampton.[1] He and his nephews John & George founded the firm of George Salter & Co., still notable makers of scales and balances, who in 1838 patented the spring balance. They also applied the same spring balance principle to steam locomotive safety valves, replacing the earlier deadweight valves.[1]

References

^ a b Hewison, Christian H. (1983). Locomotive Boiler Explosions. David and Charles. p. 18. ISBN 0-7153-8305-1.

External links

Wikisource has the text of the 1905 New International Encyclopedia article "Spring Balance".

Media related to spring balance at Wikimedia Commons
Media related to spring scales at Wikimedia Commons

Retrieved from "https://en.wikipedia.org/w/index.php?title=Spring_scale&oldid=1122470418"

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