hapter 13 Archimedes Up-thrust

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hapter 13 Archimedes Up-thrust In science, buoyancy is an upward force exerted by a fluid that opposes

Proof about the presence of Upthrust force When a block of mass 1Kg is connected to a spring balance

water, the dynamometer reads T = 7N Where does the remaining weight go to?

The force exerted by water is the difference between the real and the apparent weights.

action: vertical Direction: upwards magnitude: F up = ρ L x V i x g (will be explained soon) w F up

1 hapter 13 Archimedes Up-thrust In science, buoyancy is an upward force exerted by a fluid that opposes the weight of an immersed object. The buoyant force is also called Archimedes Up-thrust force. Proof about the presence of Upthrust force When a block of mass 1Kg is connected to a spring balance (dynamometer), the tension in the spring will read: T = w = mxg = 1x10 = 10 N But when is immersed in water, the dynamometer reads T = 7N Where does the remaining weight go to? The water held some of the weight of the block, so it appeared lighter than being held in air. The force exerted by water is the difference between the real and the apparent weights. F up = w real - w apparent Characteristics of this force: Point of application: center of mass Line of action: vertical Direction: upwards magnitude: F up = ρ L x V i x g (will be explained soon) w F up Archimedes principle says that when an object is immersed in a liquid the apparent loss of weight of an object is equal to the upthrust and this is also equal to the weight of the liquid displaced.

2 If you already know the density of the liquid then you can simply measure the volume of displaced water and use mass = volume x density to find its mass. This can easily be done using a measuring cylinder as shown in the above diagram. The origin of Upthrust force: In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus an object submerged in the fluid experiences greater pressure at the bottom of the column than at the top. This difference in pressure results in a net force that tends to accelerate an object upwards. As shown in the adjacent figure: P B > P A because it is found to be on larger depth than position A. The difference in pressure ΔP = P B - P A ΔP = F S = ρ Liquid x g x h F = ρ Liquid x g x ( h x S ) P A P B F up F = ρ Liquid x g x V immersed Where: F: Upthrust Force (N) ρ : the density of the liquid (kg/m 3 ) g: gravity = 10 N/kg V: the immersed volume inside the liquid (submerged) (m 3 ) The effect of density on Flotation Note that: The Archimedes Upthrust force depends on the density of the liquid and not the density of the object. If the density of the solid is less than the density of the liquid the object floats on the surface If the magnitude of F up is less than the magnitude of its real weight W the body will sink in a liquid. (F up <W) If the magnitude of F up is equal than the magnitude of its real weight W the body will be float on the surface in equilibrium. If the magnitude of F up is more than the magnitude of its real weight W the body will rise to the surface. (F up >W) Note: The densimeter can measure the density of a specific liquid. (a question will be given later)

3 Physics Worksheet QUESTION 1: Determination of the volume of a solid Consider a solid (S) of density ρ S = 1 g/cm 3. (S) is immersed in a liquid of density ρ. (S) is in equilibrium and the volume of the immersed part is Vi (adjacent figure). 1- (S) floats on the surface of a liquid. a) Name the two forces acting on (S). b) Tell, for each of the two forces, whether it is a contact force or an action from a distance force. c) Give the line of action and the direction of each of these two forces. d) Write down the vector relation between these two forces. e) Reproduce the figure and represent, without a scale, these two forces. 2- We repeat the experiment by putting (S) successively in different liquids. The adjacent graph represents the variation of Vi as a function of ρ. a) According to the graph, does the volume of the immersed part increase or decrease when the density of the liquid increases? b) For ρ = 1 g/cm 3, (S) is totally immersed in the liquid. Why? c) Deduce graphically the volume of (S). QUESTION 2: Floating Objects Is it easier to swim in the fresh water of a lake or in sea water? To answer this question, we perform the two following experiments with a solid (S) of mass m = 2 kg. Given: g =10 N/kg. A. First experiment (S) floats at the surface of the water of the lake of density 1000 kg/m What condition must the two forces acting on (S) satisfy so that it floats at the surface of water? 2. Calculate the value of the weight of (S). Deduce the value of Archimedes up thrust. 3. Calculate the volume V 1 of the immersed part of (S). B. Second experiment (S) floats at the surface of sea water of density 1040 kg/m 3 1. Archimedes up thrust remains the same. Why? 2. Calculate the volume V 2 of the immersed part of (S). C. Answer for the question Knowing that swimming is easier when the immersed volume of the floating object decreases, is it easier to swim in the fresh water of a lake or in the sea water? Why?

4 QUESTION 3: Determination of the density of an alcohol In order to determine the density of an alcohol, we take a solid (S) suspended from the free end of a spring balance, and two containers: one containing water and the other alcohol. Take g = 10 N/kg. I- Real weight of (S) (S) is in equilibrium in air. The spring balance indicates 8 N. This indication represents the value P of the real weight of (S). Why? II- Volume of (S) We immerse (S) completely in water of density ρ = 1000 kg/m3 (fig. 1). The spring balance then indicates 7 N. 1) What does the indication of the spring balance represent? 2) Calculate the value F of the Archimedes up thrust exerted by water on (S). 3) Deduce the volume V of (S). III- Density of the alcohol Now, (S) is completely immersed in alcohol (fig. 2). The spring balance indicates in this case 7.2 N. 1) Calculate the value F' of Archimedes up thrust exerted by the alcohol on (S). 2) Deduce the value ρ' of the density of this alcohol. QUESTION 4: A sphere (A) of mass 2.5kg & density 6250 kg/m 3 is suspended to the free end of a vertical spring whose free length is 30 cm and whose constant is 125 N/m. Take g = 10 N/kg. 1- Calculate the length of the spring when (A) is in air. 2- The sphere (A) is completely immersed in water of density 1000 kg/m 3. a) Find Archimedes up-thrust exerted by water on the sphere (A). b) Calculate the length of spring when (A) is completely immersed in water. QUESTION 5: A balloon has a mass m 1 = 0.55 kg when inflated, it contains 5m 3 of helium gas of density 0.09 kg/m 3. We attach to its lower part a mass M = 2.25 kg. The system is immersed in air of density 1.3 kg/m 3. Take g = 10 N/kg, we neglect the volume of the mass a) list the forces acting on the system S= (balloon, helium, mass) b) What is the total weight of system S? c) Find Archimedes Up-thrust by air on system (S). d) Represent the forces acting on S.

5 e) Can the system rise up (fly)? Justify your answer. QUESTION 6: A cylinder (C) of density 600 Kg/m 3 and volume 100 cm 3 is immersed in a vessel containing alcohol of density 800 kg/m 3. a) Will the cylinder (C) float in alcohol? Justify your answer. b) What are the forces acting on C? c) What is the relation between these forces? d) What is the immersed volume of (C) in the liquid? Take g = 10 N/kg. QUESTION 7: To show the dangers of icebergs on navigation, we consider a block of ice, of volume 1000 cm 3, floating on the surface of salty water as shown in the adjacent figure. Given: - Density of salty water kg/m 3. - Density of ice: 920kg/m 3. - g = 10 N/kg. 1) Explain why the block of ice floats on the surface of salty water? Dose this block float on the surface of oil having a density of 900 kg/m 3? 2) The block of ice is at equilibrium on the surface salty water. What are the forces acting on the block to maintain its equilibrium? Give the direction and the magnitude of each of these forces. 3) Find the volume of the immersed part of the block. 4) Compare the volume of the immersed part of the block to the total volume of this block. What do you conclude about the dangers of icebergs on navigation? 5) Give the name of a ship you heard about that did sink due to icebergs. QUESTION 8: A Solid (S) of mass m = 300 g floats at equilibrium at the surface of oil of density 920 kg/m 3. (S) floats at the surface of the water of the lake of density 1000 kg/m 3. A. First experiment 1) What condition must the two forces acting on (S) satisfy so that it floats at the surface of oil? 2) Calculate the value of the weight of (S). Deduce the value of Archimedes up thrust. 3) Calculate the volume V 1 of the immersed part of (S). B. Second experiment (S) floats at the surface of water of density 1000 kg/m 3 3. Is Archimedes up thrust remaining the same? Why? 4. Without calculation justify that V 2 <V 1.

6 C. Conclusion: Is there at equilibrium a relation between Archimedes up thrust force and the volume of the immersed part in liquids?justify.

storage tank, or the hull of a ship at rest, is subjected to fluid pressure distributed over its surface.

storage tank, or the hull of a ship at rest, is subjected to fluid pressure distributed over its surface. Hydrostatic Forces on Submerged Plane Surfaces Hydrostatic forces mean forces exerted by fluid at rest. - A plate exposed to a liquid, such as a gate valve in a dam, the wall of a liquid storage tank,