1. How can you prove that the force pushing out a completely submerged body is equal to the weight of the liquid in the volume of this body?
Answer: as a result of Archimedes' experiment with a bucket.
2. Does a buoyant force act on a body completely immersed in gas?
Answer: yes.
3. Archimedean force- a force that pushes a body out of a liquid or gas.
4. Why is the force that pushes a body out of a liquid or gas called Archimedean force?
Answer: in honor of the ancient Greek scientist Archimedes, who first pointed out its existence and calculated its value.
5. What contributions did Archimedes (287-212 BC) make to science?
Answer: buoyant force. For the first time he pointed out the existence of buoyancy force and calculated its value.
6. By what formula is Archimedean force determined?
7. Fill out the diagram.
8. What is the magnitude and direction of the resulting force acting on a cork float of volume V = 0.5 cm 3, completely immersed in water to a certain depth? The density of cork and water, respectively, is p t = 200 kg/m 3, p b = 103 kg/m 3.
9. A brick with a mass mk = 1.8 kg, suspended on a rope, is immersed in water. How many times will the rope's gravity change?
2) If a brick is immersed in water (see figure on the right), then in addition to the force of gravity
10. What task was set for Archimedes by the Syracusan king Hiero (200 BC)?
Answer: determine whether the crown is solid or whether there are cavities and the craftsmen who made the crown deceived him.
11. How did Archimedes solve the golden crown problem?
12. In what essay is Archimedes’ law formulated?
Answer: about floating bodies.
Lesson 48
Topic: "Archimedes' Law"
Objective of the lesson: derive a rule for calculating the Archimedean force
Lesson progress
F 1 = p 1 S 1 ; F 2 = p 2 S 2 ; since p 1 = ρ f ∙gh 1 ; p 2 = ρ f ∙gh 2 ; and S 1 = S 2 = S, where S is the area of the base of the parallelepiped. Then F out = F 2 – F 1 = ρ t ∙gh 2 S – ρ t ∙gh 1 S = ρ t ∙gS (h 2 – h 1) = ρ t ∙gS h, where h is the height of the parallelepiped.
But S h= V, where V is the volume of the parallelepiped, and ρ f V = m f is the mass of the liquid in the parallelepiped. Therefore F out. = ρ f gV = gm f = P f. , that is, the buoyant force is equal to the weight of the liquid in the volume of the body immersed in it.)
Based on this experience we can conclude: the force pushing out a body completely immersed in a liquid is equal to the liquid in the volume of this body. The same can be said about bodies immersed in any gas. The force pushing a body out of a gas is also equal to the weight of the gas taken in the volume of the body.
The force that pushes a body out of a liquid or gas is called Archimedean force, in honor of the ancient Greek scientist Archimedes, who was the first to point out the existence of buoyant force and calculate its value. Archimedes' law states: if a body is immersed in a liquid (or gas), then it loses as much weight as the liquid (or gas) it displaces weighs.
Let's calculate it based on the above experiment: the Archimedean force is equal to the weight of the liquid in the volume of the body, i.e. F A = P l = gm l. Let us express the mass of a liquid through its volume and density, i.e. m f = ρ f ∙V t. Consequently, the Archimedean force depends on the density of the liquid in which the body is immersed and on the volume of the body. Please note that the Archimedean force does not depend on the density of the substance of the body immersed in the liquid, since this value is not included in the resulting formula.
Let us now determine the weight of a body immersed in a liquid or gas. Since the two forces acting on the body are gravity and the Archimedean force are directed in opposite directions, the weight of the body in the liquid P 1 will be less than the weight of the body in vacuum P = gm (m is the mass of the body) by the Archimedean force F A = gm w ( m l – mass of liquid or gas) displaced by the body, that is, P 1 = P - F A, or P 1 = gm - gm l.
Thus:
If Archimedean force is less than gravity (F A
- if the Archimedean force is equal to the force of gravity (F A = gm), then the body will float;
If the Archimedean force is greater than the force of gravity (F A > gm), then the body will float.
1. Ice floe area – 4 m2, thickness – 0.25 m. Will an ice floe be completely submerged in water if a person stands in the middle of it and is subject to a gravity force of 700 N? The density of ice is 900 kg/m 3, the density of water is 1000 kg/m 3.
F high = ρ f gV
V= Sh = 4x0.25 = 1.0m3; F = F t l + F t w = (0.25m ∙900kg/m 3 ∙1m 3)+ (0.25m ∙1000kg/m 3 ∙1m 3)= 475N. 700N >475 N. Answer: the ice floe will not sink.
2. A concrete slab with a volume of 2 m is immersed in water. How much force must be applied to keep it in the water? In the air?
EXPERIMENTS on the topic “Archimedes’ power”
Science is wonderful, interesting and fun. But it’s hard to believe in miracles from words; you have to touch them with your own hands. There is an interesting experience!
And if you're attentive,
Independent in mind
And with physics on first hand
It's an interesting experience -
Funny, exciting -
He will reveal secrets to you
And new dreams!
1) Living and dead water
Place on the table a liter glass jar filled 2/3 with water and two glasses with liquids: one labeled “living water,” the other labeled “dead water.” Place a potato tuber (or a raw egg) into the jar. He's drowning. Add “live” water to the jar and the tuber will float; add “dead” water and it will sink again. By adding one liquid or another, you can get a solution in which the tuber will not float to the surface, but will not sink to the bottom either.
The secret of the experiment is that in the first glass there is a saturated solution of table salt, in the second there is ordinary water. (Tip: before the demonstration, it is better to peel the potatoes and pour a weak salt solution into the jar so that even a slight increase in its concentration causes an effect).
2) Cartesian pipette diver
Fill the pipette with water until it floats vertically, almost completely submerged. Place the diver's pipette into a clear plastic bottle filled to the top with water. Seal the bottle with a lid. When pressing on the walls of the vessel, the diver will begin to fill with water. By changing the pressure, get the diver to follow your commands: “Down!”, “Up!” and “Stop!” (stop at any depth).
3) Unpredictable potatoes
(The experiment can be carried out with an egg). Place the potato tuber in a glass vessel half filled with an aqueous solution of table salt. He floats on the surface.
What happens to potatoes if you add water to a vessel? They usually answer that the potatoes will float. Carefully pour water (its density is less than the density of the solution and the egg) through the funnel along the wall of the vessel until it is full. Potatoes, to the surprise of the audience, remain at the same level.
4) Rotating peach
Pour sparkling water into a glass. Carbon dioxide dissolved in a liquid under pressure will begin to come out of it. Place the peach in the glass. It will immediately float to the surface and... begin to rotate like a wheel. He will behave this way for quite a long time.
In order to understand the reason for this rotation, take a closer look at what is happening. Pay attention to the velvety skin of the fruit, to the hairs of which gas bubbles will stick. Since there will always be more bubbles on one half of the peach, a greater buoyant force acts on it, and it turns upward.
5) Archimedes' force in bulk matter
At the performance “The Legacy of Archimedes,” residents of Syracuse competed in “retrieving a pearl from the bottom of the sea.” A similar but simpler demonstration can be repeated using a small glass jar containing millet (rice). Place a tennis ball (or cork stopper) in there and close the lid. Turn the jar over so that the ball is at the bottom under the millet. If you create a slight vibration (lightly shake the jar up and down), then the friction force between the millet grains will decrease, they will become mobile and after a while the ball will float to the surface under the influence of the Archimedes force.
6) The package flew without wings
Place a candle, light it, hold the bag over it, the air in the bag will heat up,
After releasing the package, see how the package flies upward under the influence of Archimedes' force.
7) Different swimmers swim differently
Pour water and oil into the vessel. Lower the nut, plug and ice pieces. The nut will be at the bottom, the plug will be on the surface of the oil, and the ice will be on the surface of the water under a layer of oil.
This is explained by the floating conditions of the bodies:
Archimedes' force is greater than the cork's gravity - the cork floats on the surface,
Archimedes' force is less than the force of gravity acting on the nut - the nut sinks
the Archimedes force acting on a piece of ice is greater than the gravity of the ice - the cork floats on the surface of the water, but since the density of the oil is less than the density of water, and less than the density of ice - the oil will remain on the surface above the ice and water
8) Experience confirming the law
Hang the bucket and cylinder to the spring. The volume of the cylinder is equal to the internal volume of the bucket. The spring stretch is indicated by a pointer. Immerse the entire cylinder in a casting vessel with water. Water is poured into a glass.
The volume of water spilled out isOthe volume of a body immersed in water. The spring indicator marks the reduction in weight of the cylinder in water caused by the actionVbuoyant force.
Pour water from a glass into the bucket and you will see that the spring pointer returns to its original position. So, under the influence of the Archimedean force, the spring contracted, and under the influence of the weight of the displaced water it returned to its initial position. Archimedean force is equal to the weight of the fluid displaced by the body.
9) Balance has disappeared
Make a paper cylinder, hang it upside down on a lever and balance it.
Let's place the alcohol lamp under the cylinder. Under the influence of heat, the equilibrium is disturbed and the vessel rises. Since Archimedes' power is growing.
Suchshells filled with warm gas or hot air are called balloons and are used for aeronautics.
CONCLUSION
Having carried out experiments, we were convinced that bodies immersed in liquids, gases and even granular substances are acted upon by the Archimedes force, directed vertically upward. Archimedean force does not depend on the shape of the body, the depth of its immersion, the density of the body and its mass. The Archimedes force is equal to the weight of the liquid in the volume of the immersed part of the body.
We already know that the Archimedes force is the resultant of the forces of fluid pressure on all parts of the body. In Fig. 22.5, and the forces acting on areas of the same area for a body of arbitrary shape are schematically depicted. With increasing depth, these forces increase - therefore, the resultant of all pressure forces is directed upward.
Rice. 22.5. Towards a proof of Archimedes' law for a body of arbitrary shape
Let us now mentally replace the body immersed in a liquid with the same liquid, which has “hardened”, maintaining its density (Fig. 22.5, b). The same Archimedes force will act on this “body” as on this body: after all, the surface of this “body” coincides with the surface of the selected volume of liquid, and the pressure forces on various parts of the surface remain the same.
The allocated volume of liquid, “floating” inside the same liquid, is in equilibrium. This means that the force of gravity F t and the Archimedes force F A acting on it balance each other, that is, they are equal in magnitude and directed oppositely (Fig. 22.5, c). For a body at rest, the force of gravity is equal to weight - this means that the Archimedes force is equal to the weight of the allocated volume of liquid. And this is the volume of the immersed part of the body: after all, it was this that we mentally replaced with liquid.
So, we have proven that an Archimedes force acts on a body of arbitrary shape, equal in magnitude to the weight of the liquid in the volume occupied by the body.
The above proof is an example of a thought experiment. This is a favorite reasoning technique for many scientists. Galileo was especially fond of thought experiments. But the conclusions obtained as a result of a thought experiment must be verified in a real experiment: after all, with the reasoning and assumptions that are inevitable in any thought experiment, a mistake can be made. Therefore, we will not limit ourselves to the given theoretical proof of Archimedes’ law and will test it using an equally beautiful experiment.
Let's hang an empty bucket from a spring (it's called Archimedes' bucket), and from it a small stone of arbitrary shape (Fig. 22.6, a). Let's note the elongation of the spring and place a vessel under the stone into which water is poured to the level of the drain pipe (Fig. 22.6, b). When the stone is completely immersed, the water displaced by it will pour out through the pouring tube into the glass. We will notice that the elongation of the spring, due to the action of the buoyant force, has decreased.
Rice. 22.6. Experience shows that the Archimedes force is equal to the weight of water displaced by the body
Let us now pour the water displaced by the stone from the glass into Archimedes’ bucket - by doing this we will add to the weight of the stone precisely the weight of the water displaced by it. And we will see that the elongation of the spring has become the same as it was before the stone was immersed in water (Fig. 22.6, c). This means that Archimedes’ force is really equal in magnitude to the weight of the water displaced by the stone!
If we repeat the experiment, immersing the stone only partially in water, we will see that in this case the Archimedes force is equal in magnitude to the weight of the water displaced by the stone.
In laboratory work No. 9 you will be able to test Archimedes' law experimentally.
