Explanation The net force is zero when the balloon moves at terminal velocity. Therefore the upward buoyant force that is equal to the weight of the displaced air must be equal to the net downward force of the weight of the balloon material plus the weight of the helium plus the drag force at terminal velocity. F B = m balloon g + m helium g + F D (I) Here, F B is the upward buoyancy force, m balloon is the mass of balloon, m helium is the mass of the helium and F D is the drag force at terminal velocity and g is the acceleration due to gravity. Write the expression for the upward buoyant force. F B = ρ air ( 4 3 π r 3 ) g (II) Here, ρ air is the density of air and r is the radius of the balloon. Write the expression for the mass of the helium. m helium = ρ helium ( 4 3 π r 3 ) Here, ρ helium is the density of helium. Write the expression for the drag force. F D = 1 2 C D ρ air π r 2 v T 2 (III) Here, C D is the drag coefficient and v T is the terminal velocity. Write the expression for terminal velocity to travel distance h . v T = h t Here, h is the height to which balloon reaches on releasing and t is the time taken to reach a height. Substitute 1 2 C D ρ air π r 2 v T 2 for F D , ρ air ( 4 3 π r 3 ) g for F B and ρ helium ( 4 3 π r 3 ) for m helium in equation (I). ρ air ( 4 3 π r 3 ) g = m balloon g + ρ helium ( 4 3 π r 3 ) g + 1 2 C D ρ air π r 2 v T 2 (IV) Rewrite equation (IV) to get the expression for v T . ρ air ( 4 3 π r 3 ) g = m balloon g + ρ helium ( 4 3 π r 3 ) g + 1 2 C D ρ air π r 2 v T 2 1 2 C D ρ air π r 2 v T 2 = ρ air ( 4 3 π r 3 ) g − m balloon g − ρ helium ( 4 3 π r 3 ) g v<

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Density of Solids

The density of a substance refers to how much matter is present in a given amount of space. It is expressed as the ratio of the mass of the substance to its volume.

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Chapter 13, Problem 101GP

To determine

The duration for the released balloon to rise a distance h=12 m.

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Chapter 13, Problem 100GP

Chapter 13, Problem 102GP

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Chapter 13 Solutions

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Ch. 13.3 - Prob. 1AE Ch. 13.3 - A dam holds hack a lake that is 85 m deep at the...Ch. 13.7 - On the hydrometer of Example 1311, will the marks...Ch. 13.7 - Which of the following objects, submerged in...Ch. 13.7 - Which of the following objects, submerged in...Ch. 13.9 - As water in a level pipe passes from a narrow...Ch. 13.10 - Return to Chapter-Opening Question 2, page 339,...Ch. 13 - If one material has a higher density than another,...Ch. 13 - Airplane travelers sometimes note that their...Ch. 13 - The three containers in Fig. 1343 are filled with...

Ch. 13 - Consider what happens when you push both a pin and...Ch. 13 - A small amount of water is boiled in a 1-gallon...Ch. 13 - Prob. 6Q Ch. 13 - An ice cube floats in a glass of water filled to...Ch. 13 - Will an ice cube float in a glass of alcohol? Why...Ch. 13 - A submerged can of Coke will sink, but a can of...Ch. 13 - Why dont ships made of iron sink?Ch. 13 - Explain how the tube in Fig. 1344, known as a...Ch. 13 - A barge filled high with sand approaches a low...Ch. 13 - Explain why helium weather balloons, which are...Ch. 13 - A row boat floats in a swimming pool, and the...Ch. 13 - Will an empty balloon have precisely the same...Ch. 13 - Why do you float higher in salt water than in...Ch. 13 - If you dangle two pieces of paper vertically, a...Ch. 13 - Why does the stream of water from a faucet...Ch. 13 - Prob. 19Q Ch. 13 - A tall Styrofoam cup is filled with water. Two...Ch. 13 - Why do airplanes normally lake off into the wind?Ch. 13 - Two ships moving in parallel paths close to one...Ch. 13 - Prob. 23Q Ch. 13 - Prob. 24Q Ch. 13 - (I) The approximate volume of the granite monolith...Ch. 13 - (I) What is the approximate mass of air in a...Ch. 13 - (I) If you tried to smuggle gold bricks by filling...Ch. 13 - (I) State your mass and then estimate your volume....Ch. 13 - (II) A bottle has a mass of 35.00g when empty and...Ch. 13 - (II) If 5.0L of antifreeze solution (specific...Ch. 13 - Prob. 7P Ch. 13 - (I) Estimate the pressure needed to raise a column...Ch. 13 - (I) Estimate the pressure exerted on a floor by...Ch. 13 - (I) What is the difference in blood pressure...Ch. 13 - (II) How high would the level be in an alcohol...Ch. 13 - (II) In a movie, Tarzan evades his captors by...Ch. 13 - (II) The maximum gauge pressure in a hydraulic...Ch. 13 - (II) The gauge pressure in each of the four tires...Ch. 13 - (II) (a) Determine the total force and the...Ch. 13 - (II) A house at the bottom of a hill is fed by a...Ch. 13 - (II) Water anti then oil (which dont mix) are...Ch. 13 - (II) In working out his principle, Pascal showed...Ch. 13 - (II) What is the normal pressure of the atmosphere...Ch. 13 - (II) A hydraulic press for compacting powdered...Ch. 13 - (II) An open-tube mercury manometer is used to...Ch. 13 - (III) A beaker of liquid accelerates from rest, on...Ch. 13 - (III) Water stands at a height h behind a vertical...Ch. 13 - (III) Estimate the density of the water 5.4 km...Ch. 13 - (III) A cylindrical bucket of liquid (density ) is...Ch. 13 - (I) What fraction of a piece of iron will he...Ch. 13 - (I) A geologist finds that a Moon rock whose mass...Ch. 13 - (II) A crane lifts the 16,000-kg steel hull of a...Ch. 13 - (II) A spherical balloon has a radius of 7.35 m...Ch. 13 - (II) A 74-kg person has an apparent mass of 54 kg...Ch. 13 - (II) What is the likely identity of a metal (see...Ch. 13 - (II) Calculate the true mass (in vacuum) of a...Ch. 13 - Prob. 33P Ch. 13 - (II) A scuba diver and her gear displace a volume...Ch. 13 - (II) The specific gravity of ice is 0.917, whereas...Ch. 13 - (II) Archimedes principle can be used not only to...Ch. 13 - (II) (a) Show that the buoyant force FB on a...Ch. 13 - (II) A cube of side length 10.0 cm and made of...Ch. 13 - (II) How many helium-filled balloons would it take...Ch. 13 - Prob. 40P Ch. 13 - (III) If an object floats in water, its density...Ch. 13 - (III) A 3.25-kg piece of wood (SG = 0.50) floats...Ch. 13 - (I) A 15-cm-radius air duct is used to replenish...Ch. 13 - Prob. 44P Ch. 13 - (I) How fast does water flow from a hole at the...Ch. 13 - (II) A fish tank has dimensions 36 cm wide by 1.0...Ch. 13 - (II) What gauge pressure in the water mains is...Ch. 13 - Prob. 48P Ch. 13 - (II) A 180-km/h wind blowing over the flat roof of...Ch. 13 - (II) A 6.0-cm-diameter horizontal pipe gradually...Ch. 13 - (II) Estimate the air pressure inside a category 5...Ch. 13 - (II) What is the lift (in newtons) due to...Ch. 13 - (II) Show that the power needed to drive a fluid...Ch. 13 - (II) Water at a gauge pressure of 3.8 atm at...Ch. 13 - (II) In Fig. 1355, take into account the speed of...Ch. 13 - (II) Suppose the top surface of the vessel in Fig....Ch. 13 - (II) You are watering your lawn with a hose when...Ch. 13 - (III) Suppose the opening in the tank of Fig. 1355...Ch. 13 - Prob. 59P Ch. 13 - (III) (a) Show that the flow speed measured by a...Ch. 13 - Prob. 61P Ch. 13 - (III) A fire hose exerts a force on the person...Ch. 13 - (II) A viscometer consists of two concentric...Ch. 13 - Prob. 64P Ch. 13 - (I) Engine oil (assume SAE 10, Table 133) passes...Ch. 13 - Prob. 66P Ch. 13 - (II) What diameter must a 15.5-m-long air duct...Ch. 13 - (II) What must be the pressure difference between...Ch. 13 - (II) Poiseuilles equation does not hold if the...Ch. 13 - Prob. 70P Ch. 13 - (III) A patient is to be given a blood...Ch. 13 - (I) If the force F needed to move the wire in Fig....Ch. 13 - (I) Calculate the force needed to move the wire in...Ch. 13 - (II) The surface tension of a liquid can be...Ch. 13 - (III) Estimate the diameter of a steel needle that...Ch. 13 - (III) Show that inside a soap bubble, there must...Ch. 13 - (III) A common effect of surface tension is the...Ch. 13 - A 2.8-N force is applied to the plunger of a...Ch. 13 - Intravenous infusions are often made under...Ch. 13 - A beaker of water rests on an electronic balance...Ch. 13 - Estimate the difference in air pressure between...Ch. 13 - A hydraulic lift is used to jack a 920-kg car 42...Ch. 13 - When you ascend or descend a great deal when...Ch. 13 - Giraffes are a wonder of cardiovascular...Ch. 13 - Suppose a person can reduce the pressure in his...Ch. 13 - Airlines are allowed to maintain a minimum air...Ch. 13 - A simple model (Fig. 13-57) considers a continent...Ch. 13 - A ship, carrying fresh water to a desert island in...Ch. 13 - During ascent, and especially during descent,...Ch. 13 - A raft is made of 12 logs lashed together. Each is...Ch. 13 - Estimate the total mass of the Earths atmosphere,...Ch. 13 - Prob. 92GP Ch. 13 - Four lawn sprinkler heads are fed by a...Ch. 13 - A bucket of water is accelerated upward at 1.8 g....Ch. 13 - The stream of water from a faucet decreases in...Ch. 13 - You need to siphon water from a clogged sink. The...Ch. 13 - An airplane has a mass of 1.7 106 kg, and the air...Ch. 13 - A drinking fountain shoots water about 14 cm up in...Ch. 13 - A hurricane-force wind of 200 km/h blows across...Ch. 13 - Blood from an animal is placed in a bottle 1.30 m...Ch. 13 - Prob. 101GP Ch. 13 - Prob. 102GP Ch. 13 - A two-component model used to determine percent...Ch. 13 - (III) Air pressure decreases with altitude. The...

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The duration for the released balloon to rise a distance h = 12 m .

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The duration for the released balloon to rise a distance h=12 m.

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Chapter 13 Solutions