Buoyancy. Buoyancy & Archimedes Principle. Calculate the buoyant force on an object. Labs, Activities & Demonstrations:

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1 A Iportant uoyancy Page: 151 Unit: Pressure & lui Mechanics Unit: Pressure & lui Mechanics NGSS Stanars: N/A uoyancy MA Curriculu raeworks (2006): N/A AP Physics 2 Learning Objectives: 1.E.1.1, 1.E.1.2,.4.C.1,.4.C.2 Knowlege/Unerstaning: Skills: uoyancy & Archiees Principle Calculate the buoyant force on an object Language Objectives: Unerstan an correctly use the ters isplace an buoyant or buoyancy. Accurately escribe an apply the concepts escribe in this section using appropriate acaeic language. Set up an solve wor probles relating to buoyancy. Labs, Activities & Deonstrations: Upsie-own beaker with tissue Ping-pong ball or balloon uner water beaker floating in water o right-sie-up with weights o upsie-own with trappe air Spring scale with ass in & out of water on a balance Cartesian iver Aluinu foil & weights Carboar & uct tape canoes Notes: isplace: to push out of the way Use this space for suary an/or aitional notes. AP Physics 2: Algebra-ase Mr. igler

2 A Iportant uoyancy Page: 152 Unit: Pressure & lui Mechanics buoyancy: a net upwar force cause by the ifferences in hyrostatic pressure at ifferent levels within a flui: The hyrostatic pressure is stronger at the botto of the object than at the top, which causes a net upwar force on the object. When an object isplaces a flui: 1. The volue of the flui isplace equals the volue of the suberge part of the object: V V suberge Use this space for suary an/or aitional notes. 2. The weight of the flui isplace equals the buoyant force ( ).. The net force on the object, if any, is the ifference between its weight an the buoyant force:. net The buoyant force is cause by the ifference in hyrostatic pressure fro the botto of the object to the top, i.e., PA. However, the hyrostatic g pressure is a function of the epth an the area is a function of the shape of the object. y anipulating the equations an recognizing that area ties height equals volue, we get the equation for the buoyant force: V g Where is the buoyant force, ρ is the ensity of the flui that the object is suberge in, V is the volue of the flui that has been isplace, an g is the strength of the gravitational fiel (which is the sae as the acceleration ue to gravity, 10 2 ). s AP Physics 2: Algebra-ase Mr. igler

3 A Iportant uoyancy Page: 15 Unit: Pressure & lui Mechanics or those who want a calculus-base explanation, the hyrostatic force over the surface of the object is given by cobining the hyrostatic equation: P H g h with the equation for pressure, rearrange to solve for force: = PA We recognize that because the area varies with epth, this results in a ouble surface integral over the area of the object (A) an the height (h): gah g Ah Conveniently, Ah is siply the volue of the part of the object that is suberge, which is equal to the volue of flui isplace (ite #1 above). Therefore: g Ah gv This results the failiar equation for the buoyant force: Vg If the object floats, there is no net force, which eans the weight of the object is equal to the buoyant force. This eans: g g V g Cancelling g fro both sies gives V, which can be rearrange to give the equation for ensity: V If the object sinks, the weight of the object is greater than the buoyant force. This eans Vg, g g, an the weight of the suberge object is. net g Use this space for suary an/or aitional notes. AP Physics 2: Algebra-ase Mr. igler

4 A Iportant uoyancy Page: 154 Unit: Pressure & lui Mechanics Note that if the object is resting on the botto of the container, the net force ust be zero, which eans the noral force an the buoyant force cobine to supply the total upwar force. I.e., for an object resting on the botto: 0 ( ) which eans: net g N g N This concept is known as Archiees Principle, nae for the ancient Greek scientist who iscovere it. The buoyant force can be calculate fro the following equation: where: g V g = buoyant force = ass of flui isplace by the object g = strength of gravitational fiel = acceleration ue to gravity 10 on Earth) ( 2 s ρ = ensity of the flui applying the buoyant force (e.g., water, air) V = volue of flui isplace by the object Use this space for suary an/or aitional notes: AP Physics 2: Algebra-ase Mr. igler

5 A Iportant uoyancy Page: 155 Unit: Pressure & lui Mechanics Saple Probles: Q: A cruise ship isplaces tonnes of water when it is floating. (1 tonne = 1000 ) If sea water has a ensity of 1 025, what volue of water oes the ship isplace? What is the buoyant force on the ship? A: V V V (1025 )( N V g s 2 8 )(10 ) Use this space for suary an/or aitional notes. AP Physics 2: Algebra-ase Mr. igler

6 A Iportant uoyancy Page: 156 Unit: Pressure & lui Mechanics Q: Consier the following cartoon: Given the following assuptions: The balloons are stanar 11 balloons, eaning that they have a iaeter of 11 inches (28 c), which equals a raius of 14 c = The teperature is 20 C. At this teperature, air has a ensity of 1.200, an heliu has a ensity of Pasquale is probably about four years ol. The average ass a four-yearol boy is about 16. The ass of an epty balloon plus string is 2.7 g = How any balloons woul it actually take to lift Pasquale? Use this space for suary an/or aitional notes. AP Physics 2: Algebra-ase Mr. igler

7 A Iportant uoyancy Page: 157 Unit: Pressure & lui Mechanics A: In orer to lift Pasquale, = g. g g ( 16)(10) 160 N airv g ( 1.2) V (10) ecause, this eans: V V 1. g Assuing spherical balloons, the volue of one balloon is: V 4 r ( 4 )(.14)(0.14) Therefore, we nee = balloons to lift Pasquale. However, the proble with this answer is that it oesn t account for the ass of the heliu, the balloons an the strings. Each balloon contains g of heliu. Each epty balloon (incluing the string) has a ass of 2.7 g = , so the total ass of each balloon full of heliu is 1.91 g g = 4.28 g = This eans if we have n balloons, the total ass of Pasquale plus the balloons is n kilogras. The total weight of Pasquale plus the balloons is therefore this nuber ties 10, which equals n. The buoyant force of one balloon is: V g ( 1.2)(0.0115)(10) 0.18 N air Therefore, the buoyant force of n balloons is 0.18n newtons. or Pasquale to be able to float,, which eans 0.18n n n 160 n = balloons g Use this space for suary an/or aitional notes. AP Physics 2: Algebra-ase Mr. igler

8 A Iportant uoyancy Page: 158 Unit: Pressure & lui Mechanics Hoework Probles 1. A block is 0.12 wie, 0.07 long an 0.09 tall an has a ass of The block is floating in water with a ensity of a. What volue of the block is below the surface of the water? Answer: b. If the entire block were pushe uner water, what volue of water woul it isplace? Answer: c. How uch aitional ass coul be pile on top of the block before it sinks? Answer: The SS Unite Victory was a cargo ship launche in The ship ha a ass of tonnes fully loae. (1 tonne = ). The ensity of sea water is What volue of sea water i the SS Unite Victory isplace when fully loae? Answer: Use this space for suary an/or aitional notes. AP Physics 2: Algebra-ase Mr. igler

9 A Iportant uoyancy Page: 159 Unit: Pressure & lui Mechanics. An epty box is 0.11 per sie. It will slowly be fille with san that has a ensity of 500. What volue of san will cause the box to sink in water? (Assue water has a ensity of You ay neglect the weight of the box.) Answer: Use this space for suary an/or aitional notes. AP Physics 2: Algebra-ase Mr. igler