Physics question..why do bathroom scales have to be placed on a horizontal surface?

Question

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

Answer 1

Hi Essie.

 

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

 

cos(0) = 1

 

so

 

mg*cos(0) = mg*1 = mg

 

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:

 

120*cos(60) = 60 lbs

 

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,

 

cos(90) = 0

 

So the normal force in the instance would be

 

mg*cos(90) = 0

 

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.

 

Hope this helps.

Answer 2

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.