LESSON Applying Archimedes principle.

Transcription

1 LESSON Applying Archimedes principle. (4) Sketch the following graph: (a) Introduction. The figure shows a load of mass 40 N suspended in air whereas the others show the same load immersed in water at four differents depth. (b) Archimedes Principle Archimedes Principle state that When an object is immersed in a fluid (a liquid or a gas),the buoyant force ( upthrust force) on the object is equal in size to the weight of fluid displaced by the object. Estimate the spring balance readings for each figure and make the conclusion: (1) When an object is immersed partially or completely in a fluid, the weight of the object reduce and it is called as apparent weight. (2) The apparent weight depends on the weight of water dispersed/displaced. (3) The apparent weight is caused by an upward force exerted by the fluid on the object and the force is known as Buoyance Force Or Density and Buoyancy(keapungan) From Archimedes s Principle : Buoyant Force = Weight of fluid displace = mg (note : F = ma) = ρvg (note : ρ = m ) V Thus F B = ρ V g Where F B = Bouyant Force or Upthrust ρ = Density of fluid V = Volume of fluid displaced or the volume of the object that immersed in the fluid. 1

2 Example 1 Buoyant Force and Flotation A metal sphere has a volume 5 x 10-4 m 3 is immersed in water of density 1 x 10 3 kgm -3. Determine the upthrust experienced by the sphere? Example 2 A wooden block with a density 4 x 10 3 kg m -3 and a mass of 5 kg is immersed in a liquid of density 1 x 10 3 kg m - 3. Calculate the buoyant force acting on the wooden block? If Buoyant force = weight the object floats and stationary Buoyant force > weight the object moves up Buoyant force < weight the object moves down The Law of Flotation A floating object displaces its own weight of fluid in which it floats. Example 4 An object of mass 5 kg floats on the surface water. What is the upthrust experienced by the object. Example 3 An object has a weight of 40 N in air and 36 N in a liquid of density 800 kgm -3. Determine the volume of the object.ialah 36 N? 2

3 Example 5 Based on Figure (a), (b),(c) and (d) write the equations in words to relate the forces acting on the objects when the objects float and stationary. Application of Archimedes Principle (1) Ship A ship, though very heavy, floats on the surface of the sea. This is because the buoyant force = the weight of the ship. The buoyant force acting on the ship is large enough because the ship is hollow and the volume of water displaced by the ship is sufficiently large. ( F B = ρv g) The density of sea water varies with location and season. To ensure that a ship is loaded within safe limits, the Plimsoll line marked on the body of the ship acts as a guide. (2) Submarine Example 5 The figure shows a glass tube of mass kg with uniform diameter and cross-sectional area 4 x 10-4 m 2, and it is filled with sand so that it is made vertical in a beaker containing water. [ Density of water is 1000 kg m -3 ] Determine (a) The upthrust (b) The mass of sand in the glass tube. A submarine can sail on the surface or underneath it. Its outer hull is entirely watertight. Inside the hull are a number of tanks called ballast tanks which is used to control its position and depth from the surface of the sea. If ballast tanks empty Upthrust = weight submarine floats If ballast tanks full Upthrust < weight submarine sinks 3

4 (3) Hydrogen filled balloon. The balloon descends when Upthrust < Weight of hot air (helium gas) + weight of airship fabric + weight of gondola + weight of passengers The balloon remains stationary when Upthrust = Weight of hot air (helium gas) + weight of airship fabric + weight of gondola + weight of passengers A hydrogen-filled balloon will float up into the air if it is released. Air is a fluid and produces an upthrust. Density of air >>> density of hydrogen gas The balloon floats and rises upwards because Uptrust > Weight of hydrogen + weight of balloon + weight of string The balloon remains stationary in air when Uptrust = Weight of hydrogen + weight of balloon + weight of string 4) Hot air balloon (4) Hydrometer An hydrometer is an instrument used to measure the density of a liquid. It has a glass bulb which contains some lead to make it float upright, and long narrow neck with a scale marked on it caused the hydrometer more sensitive. The large air-filled glass bulb is used to displace more liquid and it caused the upthrust increases hence the hydrometer floats. In a liquid of lesser density, the hydrometer is more submerged. The hydrometer floats higher in a liquid of higher density. Density of hot air <<< density of cold air The balloon s height can be controlled by turning the gas burner which heats the air on and off as needed. The hot air balloon floats and rises upwards when Upthrust > Weight of hot air (helium gas) + weight of airship fabric + weight of gondola + weight of passengers. 4

5 TUTORIAL The figure shows a load hung from a spring balance is slowly submerged in water until it is immersed completely. 3 The figure shows four spheres, P, Q, R and S floating on water. Which comparison is correct about the density of spheres P,Q,R and S? What will happen to the spring balance reading? A zero B decreases until zero C remains unchanged D decreases until reaches a constant value 2 Which of the following figure is true? A P > Q > R > S B S > Q > R > P C P > R > Q > S D Q > R > P >S 4 A metal block has a volume m 3 is immersed in water. If the density of water is 1000 kgm -3,what is the buoyant force experienced by the metal block? A 40N B 30N C 20N D 10N E 5N 5 An object of mass 2 kg with a density of 8 x 10 3 kgm -3 is immersed in the sea water.if the density of the sea water is 1.03 x 10 3 kg m -3, what is the upthrust? A 1.2 N B 2.6 N C 3.0 N D 3.4 N E 4.0 N 6 An object has a volume 5 x 10-4 m 3 is hung from a spring balance. The reading of the spring balance is 8N.If the object is immersed fully in a liquid with a density 600 kg m -3, determine the reading of the spring balance now? A 1N B 2N C 3N D 5N E 8N 5

6 7 A body has a weight of 20N in air and 15 N in a liquid. If the volume is 5x 10-4 m 3, what is the density of the liquid? A 400 kgm -3 B 800 kgm -3 C 1000 kgm -3 D 1200 kgm -3 E 1200 kgm -3 8 Which of the following about a ship floating on the surface of sea is true? A B C D The weight of the ship equals to mass of the sea water displaced The weight of the ship equals to the weight of the sea water displaced The weight of ship is less than the weight of the sea water displaced The weight of the ship is more than the weight of the sea water displaced What is the upthrust of the balloon? A 10 N B 20 N C 100 N D 200 N E N 11 The figure shows a cube of sides 0.1 m floats in water with ¼ of its height above the water level. [ The density of water = 1000 kgm -3 ] 9 The figure shows a sphere object floating on the surface of a liquid. What is the weight of the cube? Which of the following is true? A B C D The volume of the liquid displaced by the sphere object equals to the volume of the sphere object The weight of the liquid displaced by the sphere object equals to the weight of the sphere object The mass of the sphere object equals to the mass of liquid in the container The density of sphere object equals to the density of the object 10 The figure shows a balloon of mass 200 kg is floating in a stationary position in the air. A 2.5N B 5.0 N C 7.5N D 10.0N E 12.5N 12 The figure shows a boy on a float. Which of the relationship between the physical quantities in the above situation is correct? A B C Weight of water displaced = weight of the boy + weight of the float Weight of water displaced > weight of the boy + weight of the float Volume of water displaced = volume of the boy + volume of the float 6

7 D Volume of water displaced > volume of the boy + volume of the float 13 The figure shows a boat has a safety limit line L. The volume of the boat under the line L is 4 m 3. The mass of the boat is 200 kg. [ The density of water = 1000 kgm -3 ] What is the tension,t of the string? What is the maximum load can be carried by the boat to ensure the the boat does not overload? A 2.0 X 10 3 Kg B 3.8 X 10 3 Kg C 4.0 X 10 3 Kg D 4.2 X 10 3 Kg E 5.0 X 10 3 Kg 14 The figure shows The figure shows a test tube with uniform diameter and cross-sectional area 2 x 10-4 m 2, and it is filled with sand of mass kg so that it is made vertical in a beaker containing water at a height 0.01 cm [ Density of water is 1000 kg m -3 ] A 3.0 x 10 4 N B 3.5 x 10 4 N C 4.0 x 10 4 N D 4.5 x 10 4 N E 5.0 x 10 4 N 16 Which of the following is not the application of Archimedes Principle? A Submarine B Ship C Hot air balloon D Aeroplane 17 Figure(a), Figure(b) and Figure(c) show a spring balance supporting a metal block K in three situations. (a) (b) (c) What is the mass of the test tube? A kg B kg C kg D kg E Kg 15 The figure shows a metal block has a volume 0.5 m 3 is tied to a string. The block is immersed in water. [ Density of the metal block = 8 x 10 3 kg m -3, Density of water = 1 x 10 3 kg m -3 ] (a) Compare the readings of the spring balance in Figure(a) and Figure(b) (b) Name three forces that act on K when it partially or totally in water. (c) State and explain the relationship between the forces in (b). 7

8 (d) Name the principle involved in (c) (e) (i) What will happen to the reading of the spring balance in Figure (c) if the water is replaced with salt solution? Give one reason for your answer. 18 Figure (a) shows a wooden block with load, fully immersed in water. When the load is removed, the wooden block floats as shown in Figure (b). (a) (i) Based on Figure (a), Figure (b), Figure and Figure (d), state one observation common to both the wooden block and the submarine List the forces which act on the wooden block and the submarine in Figure (b) and Figure (d).... Figure (c) shows a submarine, immersed in water with the ballast tanks filled with water. When the ballast tanks are emptied, the submarine floats as shown in Figure (4). (iii) (iv) State the relationship between the forces listed in (a). Give one reason for your answer.... 8

9 (b) Name the principle involved in the observations in Figure(a), Figure (b), Figure (c) and Figure(d).... (c) (i) What happens to the block in Figure (b) when a salt solution is added to the water?.. Give one reason for your answer A wooden block has a volume 2 x 10-3 m 3 and a density of 900 kgm - 3. Determine (a) The mass of the wooden block What is (e) The volume of the water displaced by the block at the new position? (f) The new buoyant force of the block? (b) The weight of the wooden block The wooden block is immersed partially as shown in Figure (a) and it floats in a stationary position. (g) The acceleration of the wooden block if the force is removed? What is Figure(a) 20 A large balloon is made by nylon bag is filled with 8 m 3 helium gas. (a)if the density of helium gas is 0.18 kg m -3, determine (i) the mass of the helium gas in the balloon. (c) The buoyant force of the block? (d) The volume of the water displaced by the block. [ Density of water = 1000 kg m -3 ] the weight of the helium gas in the balloon. The wooden block is later pushed by a force until the upper surface of the wooden level is same as the water surface level as shown in Figure(b). 9

10 (b) The figure shows the ballon later is tied by a nylon string and a load of mass 3.65 kg hung at the other end of the string.the balloon floats in a fix height. [ The density of air =1.25 kg m -3 ] 21 (a) A fisherman finds that his boat is at different levels in the sea and in the river, although the boat carries the same load. The density of sea water kg m -3 and of river water is kg m -3. Figure(a) and Figure(b) illustrate the situation of the boat in the sea and in the river (i) What is he resultant force acting on the balloon? (c) Calculate the buoyant force acting on the balloon. Determine the mass of the nylon bag. When the string attached to the load snaps, (i) What is the acceleration of the balloon. What will happen to the motion of balloon when the height of the balloon increases? (b) (c) (i) What is meant by density? Using Figure(a) and Figure(b), compare the levels of the boat and the volumes of water displaced by the boat. Relating the mass of the boat with its load, the volume of water displaced and the density of the water, deduce a relevant physics concept. (iii) Name the physics principle that explains the above situations. A submarine can sail on the sea surface and under the sea. Explain how a submarine on the surface submerges. Figure(c) and Figure (d) illustrate the working principle of a hydrometer. The depth to which the test tube sinks depends on its surrounding liquid. 10

11 22 Figure(c) Figure(d) Explain how you would design a hydrometer that can determine a wide range of densities of liquid, using the idea of the working principle of a hydrometer shown above. Draw a diagram that shows the design of your hydrometer and in your explanation, emphasize the following aspects: (i) the stability of the hydrometer the sensitivity of the hydrometer (iii) the ability to measure a wide range of densities of liquids (iv) the calibration of the hydrometer Easy topull the fishing net Figure (a) More difficult to pull the net Figure(c) Figure (a), Figure (b) and Figure (c) show three different situations when a fisherman is pulling a fishing net from the sea. In Figure (a), the fisherman finds it easy to pull a fishing net while most of the net is in the water. However, the fisherman finds it difficult as the fishing net is emerging from the water surface as shown in Figure (b) and Figure (c). Based on the observations: (a) State one suitable inference that can be made. (b) State one appropriate hypothesis for an investigation. (c) With the use of apparatus such wooden rod, spring balance,beakerand other apparatus, describe an experimental framework to test your hypothesis. In your description, state clearly the following: (i) Aim of the experiment Variables in the experiment (iii) List of apparatus and materials (iv) Arrangement of the apparatus (v) The procedure of the experiment which include the method of controlling the manipulated variable and the method of measuring the responding variable. (vi) Way you would tabulate the data (vii) Way you would analysis the data Difficult pull the fishing net Figure(b) 11