 Here we're going to be looking at what a spring scale measures. Now you may think well, that's pretty simple It just measures weight, but it's not quite that simple. Let's take a closer look This scale has a spring built into the plastic housing here when you put a weight on the scale the spring stretches and That causes the needle to deflect and give you a reading in terms of newtons now the object that we're going to be weighing is this Soda pop bottle that we filled with sand It has a mass of about one kilogram. So it's weight should be about 9.8 newtons and As you can see from the scale reading it's right around 10 newtons now we're going to look at the forces acting on the Scale in this situation and go from there We begin by representing the bottle of sand with a point There are two forces acting 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 Mg To set up a net force equation we need to define a positive direction Normally that would be in the direction of the acceleration, but in this case the bottle of sand is not accelerating So we can choose either up or down. I'll choose up for positive The next step is to write the net force equation f net equals Now the upward force is T and that will be positive So I'll write that first and the downward force is Mg and that's negative So that will be subtracted from T now since the Object the bottle of sand is not accelerating The net force acting on it is zero and therefore we can say that the tension force is Equal to Mg the weight of the bottle so in this particular case the spring scale measures The weight of the bottle So we've seen that to keep the object in equilibrium. I have to exert a force upward that's equal to the object's weight Now you may have noticed that as I've been holding this the needle has been oscillating back and forth around 10 So since the needle is reading different things even while I'm holding the same bottle here There must be something involved other than just the weight of the bottle That thing has to do with the fact that I can't hold the scale perfectly steady So I'm exerting small accelerations on it up and down Let me exaggerate that by pulling the scale up quickly So I'll give it a quick upward acceleration you watch what the needle does as soon as I pull Now at the SNI pulled you saw the needle go up Now at some point when I came to a stop the needle also came to a stop and came back down again Let's concentrate first on that first part where I did the upward pull. Let me do it one more time Okay, now we're going to go back and look at the forces there and do a force analysis for this situation For this situation we applied a greater tension force in order to achieve an upward acceleration The net force equation will look the same as it did before Because we still have a tension force and a weight force We still have the direction of positive up and so f net equal t minus mg What's different is that the net force is no longer zero Because the acceleration is not zero the net force by Newton's second law is the mass of the object times its acceleration This is equal to the tension force minus the weight Solving this for the tension force We get t equal mg plus ma So we find that the reading of the spring scale, which is the tension force in this case is Equal to the true weight of the object plus the mass of the object times its acceleration So what we saw with the force analysis was that the scale reads the tension force in The case of equilibrium that I have here that tension force is simply equal to the weight of the object But when I was accelerating upward that tension force was equal to the weight of the object mg Plus the mass of the object times its acceleration or mg plus ma We call that the apparent weight of the object in other words what the scale measures the tension force is The apparent weight the true weight would be mg the apparent weight in this case is mg plus the mass of the object times its acceleration Now let's take a look at the situation where we lower the scale quickly in other words We give it a downward acceleration watch closely when I do this We do that one more time All right What you probably saw was as soon as I started to lower it the needle moved this way very quickly So the reading went down of course it came to a stop when I came to a stop and went back the other direction What I want you to do now is to work on your papers to do the force analysis for this situation Set it up like I did the case for the upward acceleration draw your forces write your net force equation Remember this time though that the acceleration is down instead of up Therefore when you pick the direction of positive pick that direction to be down Solve for the tension force and then we'll take a look at what you have