# Fluids I. Level : Conceptual Physics/Physics I. Q1) Order the following materials from lowest to greatest according to their densities.

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1 Fluids I Level : Conceptual Physics/Physics I Teacher : Kim 1. Density One of the properties of any substances (solids, liquids and gases) is the measure of how tightly the material is packed together. This property is called density. Density is a measure of how much matter is squeezed into a given space, that is, the amount of mass per unit volume. density = mmmmmmmm vvvvvvvvvvvv [kg/m3 ] Q1) Order the following materials from lowest to greatest according to their densities. water blood Earth s core seawater interstellar-space Sun s core Earth s crust black-hole Q2) i) What is the density of an object of mass 12kg and a volume of 4m 3? m=12kg, volume=length width height = 4m 3 ii) What is the mass, volume and density if we break the object in half? 2. Pressure Demo1) Hold a weight(50g) and a sponge ball. Observe which object feels heavier. i) Weight feels heavier! ii) Sponge ball feels heavier! Demo2) Hold a book in three different ways as below. Which case seems heaviest? i) flat on your hand ii) upright on your hand iii) only the corner on your hand

2 How much press we feel from the book depends in the area of contact for each case. That is, the amount of force per unit area is called pressure. pressure= ffffffffff ssssssssssssss aaaaaaaa P= FF AA where P is the pressure and A is the area over which the force acts The unit for pressure is pascal(pa). One Newton per square meter is equal to one pascal. That is, 1N/m=1Pa Q3) A cube is lying on the floor. If the mass of the cube is 2kg, find the pressure the cube is exerting on the surface of the floor. (weight is F g=mg, where g=9.8m/s 2 ) 0.2m 0.2m 0.2m 3. Liquid Pressure according to depth Liquid has weight(=force), so it must also exert pressure. Q4) Compare the following two situations. Case1) You are swimming 1 meter deep in an Olympic size pool Case2) You are swimming 1 meter deep in an ocean In which case would you feel more pressure? - Liquid pressure depends only on the density and the depth of the liquid, not on the shape or size of its container. - Liquid pressure does not depend on the amount of liquid - Liquid does not compress, so the density at the surface or bottom of a lake approximately the same Pressure due to liquid = (weight) density depth

3 Q5) Why dams are built thicker at the bottom? Large, but shallow lake Small, but deep lake 4. Buoyancy Why do object weigh less in water than on air? When an object is submerged in water, the water exerts an upward force that is opposite in gravity. This upward force is called buoyant force Try pushing a volley ball into water. The water will try to push back on the volley ball back up to the surface. That pushing back force is the buoyant force Q6) Explain why water exerts an upward force on objects in the water. (hint: remember that liquid pressure exerted on an object varies according to depth only) Q7) Buoyant force and weight are both forces. If one is acting greater than the other on an object, the object will move in that direction. Connect the statement for each case. If the weight of a submerged object is greater than the float buoyant force, then the object will the weight of a submerged object is less than the buoyant stay still force, then the object will the weight of a submerged object is equal to the buoyant sink force, then the object will Q8) A bowling ball has a diameter of 21.8cm. A volley ball has a diameter of 20.7cm to 21.3cm. If the two balls are pushed completely under water and then released, the volleyball will float back up while the bowling ball will sink. Which statement is true? a) the buoyant force acting on the bowling ball is less than the volleyball b) the buoyant force acting on the bowling ball is greater than the volleyball c) the buoyant force acting on the bowling ball is similar than the volleyball

4 The following statement is false. The buoyant force acting on a floating object is always stronger than the buoyant force acting on a sinking object The buoyant force that acts on a completely submerged object is determined by the weight or mass of the object The buoyant force that acts on a completely submerged object equals the weight of the object To further understand buoyancy, we need to see what happens when an object is placed in water. - If a stone is placed in a container of water, the water level will rise because the stone pushes the water aside. - How much water is pushed away(=displaced) is determined by the volume of the object, and irrelevant to the weight, mass, color, smell etc, of the object. - The amount of water displaced is equal to the volume of the stone the amount of liquid =volume of the stone - A completely submerged object always displaces a volume of liquid equal to its own volume. And the more liquid the object displaces, the stronger the buoyant force. 5. Archimede s Principle *~An immersed object is buoyed up by a force equal to the weight of the fluid it displaces. Archimede s principle = Newton s 3 rd law If you put something in water that pushes 100N of water out of the way(=displaces 100N weight of water), then the water pushes back with a force of 100N. The buoyant force is equal and opposite to the weight of water you displace What does the above principle mean?!! - A liter is a measure of volume. 1-liter is equal to the volume of a cube with 10cm sides - If you immerse 1-liter container into water, whether the container is empty or filled with anything, the container will displace 1 liter 10cm volume of water, 10cm - If we weigh that 1-liter of water on a scale, it will weigh 9.8N. Since the buoyant force is equal to the weight of water being displaced, the buoyant force acting on the 1-liter container filled with anything will always be 9.8N in water 10cm

5 - If we immerse an empty 1-liter container in water, the empty container will float since the buoyant force is greater than the empty container. - If we fill the 1-liter container with water and immerse it into water, the container will stay still in the water, since the buoyant force is equal to the water-filled container.(that is, if we assume the mass of the container itself is very light) - If we fill the 1-liter container with mercury(which is more dense and heavier than water) and immerse it into water, the container will sink, since the buoyant force is less than the mercuryfilled container. - If we fill the 1-liter container with water and immerse it into pool of mercury, the container will float, since the buoyant force is greater than the water-filled container. - If we fill the 1-liter container with mercury and immerse it into pool of mercury, the container will stay still, since the buoyant force is equal to the water-filled container. A liter of water has a mass of 1kg and weighs 9.8N. Any object with a volume of 1 liter will experience a buoyant force of 9.8N when fully submerged - If we immerse a sealed 1-liter container halfway into water, it will displace half a liter of water. - If we immerse it all the way, it will be buoyed up by the weight of a full liter of water(about 9.8N) - The buoyant force will equal the weight of 1 liter of water at any depth( **water is incompressible, so density is the same in any depth) - The container will displace the same volume of water, and hence the same weight of water at any depth - The weight of this displaced water( not the weight of the submerged object!!) is the buoyant force Caution!! The buoyant force that acts on a submerged object is irrelevant of the mass or weight of that object. It is only determined by the volume of the object. Q9) A 1-liter container filled with mercury has a mass of 13.6kg and weighs 133N. When it is submerged in water, what is the buoyant force on it? Will it float, sink or stay still in the water?

6 Q10) A block is held suspended beneath the water in three positions. In which position is the pressure the greatest? In which position is the buoyant force the greatest? Explain!! A B C Additional Question A 1-liter container filled with water has a mass of 1kg and weighs 9.8N. A 1-liter container filled with mercury. A 1-liter container filled with mercury has a mass of 13.6kg and weighs 133N. Use the information above to answer the following questions. 1. What is the buoyant force acting on an empty 1-liter container when submerged into water? Will it float, sink or stay still in the water? Justify your answer~! 2. What is the buoyant force acting on a 1-liter container filled with mercury liquid when submerged into water? Will it float, sink or stay still in the water? Justify your answer~! 3. What is the buoyant force acting on an empty 1-liter container when submerged into mercury liquid? Will it float, sink or stay still in liquid mercury? Justify your answer~! 4. What is the buoyant force acting on a water-filled 1-liter container when submerged into mercury liquid? Will it float, sink or stay still in liquid mercury? Justify your answer~!

7 6. Sink or Float? Q11) Heavy objects sink in water, while light objects float. True or false? The buoyant force on a submerged object depends on the how much water is displaced by the object = The buoyant force on a submerged object depends on the object s volume A smaller object displaces less water, so a smaller buoyant force acts on it A larger object displaces more water, so a larger buoyant force acts on it => The submerged objects volume, not its weight, determines the buoyant force!! 7. Floatation When primitive people observed that wood floats on water, they made their boats of wood. Could they have conceived of an iron ship? The idea of floating iron might be seem strange and impossible at that time since iron sinks, but today we see huge ships made of iron that floats. *~How to make iron float Consider a solid 1-ton block of iron. Iron is nearly 8 times denser than water, so a block of iron will sink. So how can we make that piece of iron float? Since iron is so dense, the weight of water it displaces will be no match for the weight of the iron. That is, the buoyant force is less than the weight of the piece of iron. = sink However, if we shape the iron into a bowl shape, we can increase the amount of water it displaces. This will increase the buoyant force acting on the iron. sink!! float!! *The principle of floatation* A floating object must displace a weight of fluid equal to its own weight =>Every ship must be designed to displace a weight of water equal to its own weight Ex) A ton ship must be built wide enough to displace tons of water before it sinks too deep below the water

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