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Physics 213 class discussions

Please answer each question since our teacher did a poor job of not only explaining each situation(1-5), but did not give pictures on the chalk board of forces, etc or to see what is visually going on. Please add anything to help me learn please!

Choose the correct answer or state not enough information if the answer could depend on circumstances not specified. Justify your answer in each case. If there isn't enough information, explain that as well. In all cases the objects are touching the walls of the beakers, and they touch the bottom only if they sink.

1) Two objects of mass 250g each are placed in two identical beakers with identical amounts of water. The objects are different: one floats and the other sinks. Which beaker shows a larger rise in level, the one with the floater, the one with the sinker, or both the same?
2) Now the floater is placed in yet another identical beaker, filled to the same level, but with oil(oil floats in water). It still floats. Does the level rise more, less or the same as when the same floater was placed in water?
3) Now the floater is placed in yet another identical beaker, filled to the same level, but with alcohol(alcohol floats in water). Now it sinks. Does the level rise more, less or the same as when the same floater was placed in oil?
4) Now the sinker is attached to a string to a half inflated (with air) balloon. The whole assembly now has a mass of 251g. The system is placed in the same beaker it was before(with the same water) and it floats with the balloon almost entirely under water. Does the level rise more, less or the same as when the same sinker was alone in the beaker ?
5) Now the balloon is inflated with air with the sinker still attached, and the system is again placed in the same beaker (the beaker is big enough for the balloon not to touch he lips.) The system floats with a small fraction of the balloon under water. Does the level rise (at least slightly) more, (at least slightly) less or (exactly) the same as it did with the half inflated balloon?

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Physics 213 class discussions

Please answer each question since our teacher did a poor job of not only explaining each situation(1-5), but did not give pictures on the chalk board of forces, etc or to see what is visually going on. Please add anything to help me learn please!

Choose the correct answer or state not enough information if the answer could depend on circumstances not specified. Justify your answer in each case. If there isn't enough information, explain that as well. In all cases the objects are touching the walls of the beakers, and they touch the bottom only if they sink.

Buoyancy
In physics, buoyancy is an upward force on an object immersed in a fluid (i.e. a liquid or a gas), enabling it to float or at least to appear to become lighter. If the buoyancy exceeds the weight, then the object floats; if the weight exceeds the buoyancy, the object sinks. If the buoyancy equals the weight, the body has neutral buoyancy and may remain at its level. If its compressibility is less than that of the surrounding fluid, it is in stable equilibrium and will, indeed, remain at rest, but if its compressibility is greater, its equilibrium is unstable, and it will rise and expand on the slightest upward perturbation, but fall and compress on the slightest downward perturbation. It was the ancient Greek, Archimedes of Syracuse, who first discovered the law of buoyancy, sometimes called Archimedes' principle:

The buoyant force is equal to the weight of the displaced fluid.

Typically, the weight of the displaced fluid is directly proportional to the volume of their displaced fluid (Specifically if the surrounding fluid is of uniform density.) Thus, among objects with equal masses, the one with greater volume has greater buoyancy.
Suppose a rock's weight is measured at 10 Newton when suspended by a string in a vacuum. Suppose that when the rock is lowered by the string into water, it displaces water whose weight is 3 Newton. The force it then exerts on the string from which it hangs will be 10 Newton minus the 3 Newton of buoyant force: 10 - 3 = 7 Newton.
Buoyancy is the underlying principle of many vehicles such as boats, ships, balloons, and airships.
Density
If the weight of an object is less than the weight of the fluid that the object would displace if it was fully submerged, then the object is less dense than the fluid and it floats at a level so it displaces the same weight of fluid as the weight of the object.
An object made of a material of higher density than the fluid, e.g. a metal object in water, can still float if it has a suitable shape (e.g. a hollow which is open upwards or downwards) that keeps a large enough volume of air below the surface level of the fluid. In that case, for the average density mentioned above, the air is included also, which may reduce this density to less than that of the fluid.

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The rise in the level of water is due to the space required for the solid object within water. The water equal to volume of the sunken part of the solid is displaced and goes up giving rise to the increase in the level of the surface of water in the beaker

1) Two objects of mass 250g each are placed in two identical beakers with identical amounts of water. The objects are different: one floats and the other sinks. Which beaker shows a larger rise in level, the one with the floater, the one with the sinker, or both the same?

Now the object, which is floating has displaced water equal to its weight 250g, but the other is sunk displacing water less then 250 gm. hence the rise in the level of water in the beaker with floating object will be higher.

The beaker with floater shows a larger rise in level.

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2) Now the floater is placed in yet another identical beaker, filled to the same level, but with oil(oil floats in water). It still floats. Does the level rise more, less or the same as when the same floater was placed in water?

The oil floats over water means the density of the oil is less then the density of water, means the oil is lighter then water so the volume of 250g of oil is more then the volume of 250g water therefore the displaced oil will have larger volume and the rise in the level is larger. Hence

The level rise more as when the same floater was placed in water.
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3) Now the floater is placed in yet another identical beaker, filled to the same level, but with alcohol(alcohol floats in water). Now it sinks. Does the level rise more, less or the same as when the same floater was placed in oil?

In both previous cases the object was floating on the surface means the volume of the displaced liquid was less then the volume of the floater (as some part is above the surface of the liquid). When the object sinks in alcohol the volume of alcohol displaced is equal to the volume of the object, hence larger volume of the alcohol is displaced in this case as compared to previous cases and the level will be still higher.

The level rise more as when the same floater was placed in oil.

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4) Now the sinker is attached to a string to a half inflated (with air) balloon. The whole assembly now has a mass of 251g. The system is placed in the same beaker it was before(with the same water) and it floats with the balloon almost entirely under water. Does the level rise more, less or the same as when the same sinker was alone in the beaker ?

In the first case the mass of the water displaced was less then 250g but now the sinker and the balloon both are displacing water of mass 251g and hence the rise in level will be more.

The rise in the level will be more as when the sinker alone was in water.

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5) Now the balloon is inflated with air with the sinker still attached, and the system is again placed in the same beaker (the beaker is big enough for the balloon not to touch he lips.) The system floats with a small fraction of the balloon under water. Does the level rise (at least slightly) more, (at least slightly) less or (exactly) the same as it did with the half inflated balloon?

In this case the mass and weight of the balloon is more as in previous case (251g) because of additional air and hence the mass of the water displaced is slightly more as compared to the previous case and hence the rise in the level will be more.

The rise in the level will be slightly more as when the sinker was with half inflated balloon.

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