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What Does a Spring Scale Measure, Part 1

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We are going to see what a spring scale measures. You may be thinking, oh that's simple, it measures weight. But its not quite that simple. Let's take a close look. This scale has a spring built into the plastic housing. When you put a weight on the scale, the spring stretches and causes the needle to deflect, and give you a reading in Newton's.

Now the object that we are going to be weighing is this soda pop bottle that we filled with sand. It has a mass of about one kilogram, so its weight should be about 9.8 Newtons. As you can see from the scale reading, it is right around there.

Now we are going to look at the forces acting on this scale, and go from there.

We begin with the soda bottle as a point. There are two forces on the bottle, one is the tension force of the scale, acting upward, the other is the weight, of the bottle of sand, acting downward. To set up a net force equation, we need to define a positive direction. Normally that would be in the direction of acceleration. The bottle of sand, however, is not accelerating, so I'll choose a direction. I'll choose up for positive. Next step is to write a net force equation. Now the upward forces is T, so I'll write that first. And the downward force is mg, so that will be subtracted from T. Now since the object is not accelerating, the net force is 0. So we can say that T is equal to mg. So in this particular case, the tension force measures the weight of the bottle.

So we see that keep the object at equilibrium, I have to apply a force upward that is equal to the objects weight. Now you may have noticed that the needle has been oscillating back and forth. Since the needle is reading different things, there must be something involved other than the acceleration of the bottle. That's because I cant hold the spring scale perfectly still, I'm applying small accelerations up and down. Let me exaggerate that by pulling the scale up quickly. Watch what the needle does when I pull it up. Now the instance I pulled you saw the needle go up. Now at some point, when I came to a stop, it also came to a stop, and came down again. Let's concentrate first on that first part again where I did that upward pull. And now we are going to go back and do a force analysis for this particular situation.

For this situation, we applied a greater tension force in order to achieve upward acceleration. The net force equation will look the same as it did before. We still have a Tension force, and a weight force. We still have a direction of positive up. What's different is the net force is no longer zero, because the acceleration is no longer zero. By Newton's second law, the net force is the mass of the object * the acceleration of the object. This is equal to T-mg. Solving for T, we get T = ma+mg. So we find that the reading of the spring scale, in this case, is equal to the true weight of the object plus the mass of the object * its acceleration.

So what we saw with the force analysis is the scale measures Tension force. In the case of equilibrium, the Tension Force is equal to the weight of the object. But when I was accelerating upward, the Tension force was equal to the weight of the object plus ma. We call this the apparent weight of the object. In other words, what the scale measures, Tension force, is the apparent weight. The true weight would be mg. The apparent weight is mg + the mass of the object * the acceleration.

Now let's take a look at a situation where we quickly lower the object. In other words we give it a downward acceleration. What you probably saw was when I started to lower it, the needle started to move this way. What I want you to do now is work on your papers, do a force analysis for this situation. Set it up like I did for the upward situation, write your net force equation, draw your forces. Remember this time that the acceleration is down rather than up. Therefore, when you pick the direction of positive, choose that direction to be down. Solve for the tension force, then we will take a look at what you have.

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