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How to calculate the king's crown using buoyancy...

Question

How to calculate the king's crown using buoyancy

How to calculate the king's crown using buoyancy



Answers

Estimate the buoyant force that air exerts on you. (To do this, you can estimate your volume by knowing your weight and by assuming that your weight density is a bit less than that of water.)

Attention. Thus the brand force. It was n g the weight So tension can be read in as f. W. Thus why enforces? Density of the water wasn't of the drowned. That's G. It was M G O W. So from here we have one minus. If trans W job, you can believe that rope round we ground G equals role water. We ground G. So from here, this part's cancel out. We find no water over the crown or the other way around. No crown over water is 1/1 minus f. So hence no. Now the question is if the family started Golden West 12.9 New trend in air What is this way when discomfited the immersed in the water? So it's where it would be. In that case, it's actually weighed row crown. We ground G minus the blind for several water. We ground G. It was roll around minus water times one with the crown times G and putting the numbers in. We will have this to be 11.8 new gun

So we're looking to find the apparent weight of the crown in water if the crown is 100% gold. So we'll start with writing that the weight apparent weight and water is equal to the gravitational force minus the buoyant force. And then the gravitational force is equal to the mass. The Crown times The gravitational constant in the buoyant force is equal to the density of water times the volume of water displaced which is equal to the volume of the crown in this case times the gravitational constant. Now we know that the volume of the crown is equal to the mass, the crown divided by the density of the crown. So we can rewrite this as mass times gravitational constant, minus intensity of water times the mass, the crown over the density of the crown times the gravitational constant. Now we plug in our values. I have written in black. On the left we get a value of 12.3 Newtons for the apparent weight of the crown in water when it is 100% gold. But for Part B, we have a different value for the density since it's 75% gold and 25% silver. To calculate the new density of the crown. We just take 0.75 times the density of gold plus 0.25 times the density of silver and we get a value of 17.1 grams per centimeter. Cute. Then, if we plugged that into our equation, we have right here. We find that the weight is equal to 10.7 Newtons. So if the crown is 75 present gold and 25% silver, it's apparent weight and water will be 10.7 Nunes.

So as destined to find your volume by dividing your waiting mutants by waters. Way density. Now wait. Density off water is given as 9800 Newtons per meter. Duke. Ah, we found that in the textbook. Now the boon pours is basically the weight displaced, the weight of the displaced here. So we have to multiply the volume, by the way, density off here so and also from textbook we see that way density of air is 12 mutant per meter cube. So, for example, if your weight is for 90 on Newton's, which is roughly 110 pounds, then your volume will be 4 90 over 9800 with the 0.5 meter cube. Now, to find the bone force we call be dot f It is a boon force. We have to multiply the volume with the weight density off air and to do. After doing that, we see that the burn forces 0.6 mutants, which is roughly a weight off a large egg. Thank you

Galileo thermometer works based on the principle of when a knob decked has the same density as a solution in which it is placed that it remains suspended in the solution at any location. If, however, the density of the object is greater, it sinks to the bottom if the density is less than it floats on top. So a Galileo thermometer than contains typically an organic liquid that has a density that will change more significantly with temperature than the objects placed into the fluid, the objects placed into the fluid then often I have different colors just to represent the temperatures at which they will remain suspended. But more specifically, the different colors correspond to be different densities. Associating with each of the objects the fluid in which everything is suspended does not have to be ethanol. It could be water. The objective is to just make sure that the density of the fluid changes with temperature more than the density of the objects that are placed in the fluid. These objects have counterweights in order to slightly change their densities by adding more mass, maintaining the volume relatively constant. These counterweights then typically have a temperature hanging on them, which will correspond to the temperature at which the density of the object is equal to the density of the fluid in which it is suspended. So as the temperature changes, then attempt the density of the fluid changes more than the objects. You could assume that the density of the object stayed constant and as we increase temperature than the density of fluid is going to decrease, and as we decrease temperature, the density of the fluid will increase. At this particular temperature. The density associated with the green object is less than the fluid. The density of the red object is equal to fluid as it is suspended somewhere in the fluid, and then these two objects down below have a density of this particular temperature greater than the fluid.


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