# How acceleration upwards and downwards affects force

1. Jun 13, 2012

### lokifenrir96

Hi, I found two physics questions, and I'm still quite confused how this works:

If a spring balance is attached to a weight, and the spring balance is then attached to the top of an elevator (on the inside), then it reads the force exerted by the weight downwards. But when the lift accelerates upwards, somehow the reading on the spring balance increases. I just see it as the spring balance having to exert a force (?) or upwards to accelerate upwards together with the elevator, so the reading increases...

For the other question, it's a weighing scale on the bottom of the elevator. There's a weight on top of it, and it reads a certain weight. When the lift accelerates upwards, the reading increases. I was wondering why, though.

Yeah, basically, I'm confused over why acceleration up and down would increase the readings of these instruments used to measure weight... Can someone explain this to me? Thanks!

2. Jun 13, 2012

### lokifenrir96

Taking a guess:

Since the instruments are attached to the elevator in some way, then as the lift accelerates upwards, the instruments would accelerate as well. By F=ma, they exert a force upwards. So for the weighing scale, it exerts a force upwards on the object. So the reaction force is exerted by the object on the weighing scale, causing the reading to increase. For the spring balance, the balance exerts an upward pulling force on the weight, so the weight exerts a reaction force downwards?

I'm not sure if this is correct, though...

3. Jun 13, 2012

### Ken G

Yes, that's correct-- the weight will stretch the spring until the spring force increases enough to accelerate the weight along with the elevator (not worrying about transient oscillations that may also appear).
Same answer-- the scale cannot allow the object to penetrate into it, so must create an increased force, until the object is accelerating with the elevator. More than likely it is a spring in there that is getting compressed-- compressed springs work a lot like stretched springs, they just push instead of pull.
Your examples were all about accelerating upward, a downward acceleration would reduce the readings on both scales because the scale needn't balance the full force of gravity on the object if the object is accelerating downward with the elevator. It sounded like you understood the hanging case, so you just need to think about how a compressed spring acts a lot like a stretched spring, it just makes a force in the opposite direction.

Perhaps there is also some confusion about the meaning of "measuring weight." A spring isn't a way of measuring weight unless there are some other assumptions being met-- all a spring does is exert a force based on whether it is stretched or compressed. We usually reserve the term "weight" for "force of gravity", so if we take that meaning, than a scale in an accelerating elevator simply doesn't measure weight any more, it just measures the force being exerted by the spring. However, some people take the meaning of "weight" to be "whatever the scale is reading", but in that case, it is no longer the force of gravity on the object (because it includes the need to accelerate the object). So part of your confusion might be around the way the term "weight" is not always used in a consistent way.

4. Jun 13, 2012

### lokifenrir96

Wow thanks! So... I take it my guess regarding action and reaction forces is wrong, then?

5. Jun 13, 2012

### jbriggs444

A "spring balance" is not a valid type of weighing device. You can have a spring scale
or a balance scale. But a spring balance... not so much.

Let us assume that you are talking about a spring scale.

A spring scale measures force. A simple spring scale does this by measuring the deflection
on a spring and uses Hooke's law to equate the observed deflection of the spring to an inferred force applied by the object to the scale. When you read the scale, you wait until it steadies down with the object supported by the scale alone so that the object is stationary with respect to the scale.

Newton's third law assures you that the downward force of the object on the scale is equal to the upward force of the scale on the object. That is where you might reason about "action" and "reaction" forces.

Newton's second law assures you that the acceleration of the object is proportional to the net external force on that object.

If the object is stationary with respect to the scale and the scale is stationary with respect to the elevator and if the elevator is stationary then the acceleration of the object is zero. This means that the net force on the object is zero. This means that the force on the scale is equal to the force of gravity on the object. This in turn means that the scale's measurement accurately reflects the force of gravity on the object.

However, that is not the situation in the case at hand.

If the object is stationary with respect to the scale and the scale is stationary with respect to the elevator and if the elevator is accelerating upward, that means that the object is accelerating upward.

If the object is accelerating upward, that means that the supporting force on the object from the scale must exceed the force of gravity on the object. Since what the scale is measuring is the third law partner force for the supporting force, the scale's reading must be greater than the weight of the object.

If the elevator is accelerating downward, the same reasoning applies and the scale will measure something less than the full weight of the object.

If you were using a balance scale to measure weight then you have different behavior [and some semantic issues about just what it is that you are measuring]. But I don't believe that you are asking about balance scales here.

6. Jun 13, 2012

### Ken G

Actually, it sounded pretty reasonable to me, I just thought I'd fill in some details.