1
$\begingroup$

Let's say hypothetically that I'm standing on a scale while holding an object with some mass. If I accelerate the mass upwards (with my hands), will the reading on the scale increase? I've been thinking about this scenario and I can't seem to figure this out.

I know that a scale's reading is just the Normal Force it exerts, but how would $F_N$ change if I accelerate an object upwards?

$\endgroup$
3
$\begingroup$

To accelerate the mass (and your hand and arm) will require an upward force provided by the rest of you.
Thus, there is an equal magnitude downward force on the rest of you - Newton’s third law.
This force is transmitted to the rest of your body, and your weight will be acting on the scale which in turn must exert an equal magnitude upward force on the rest of your body.
This upward force is the normal reaction force on the rest of your body due to the scales which will result in a higher reading on the scales i.e. a spring in the scales will have to be compressed more to provide the extra upward force.

$\endgroup$
2
$\begingroup$

When you apply an upward force on the mass, it provides an equal and opposite downward force on you. You then apply the same downward force on the scale, which results in an equal and opposite upward force on you a reflected by an increase in the scale reading (ΔN), all in accordance with Newton’s third law. Try it out. See the diagram below.

If you have a scale, stand on it holding, say, a stack if dishes. Thrust them upward and watch the scale reading temporarily increase. The reverse is also true. Let them rapidly fall in your hands and watch the scale reading temporarily decrease.

Hope this helps. enter image description here

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.