Physics for Scientists and Engineers, Technology Update (No access codes included)
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 14, Problem 14.78AP

Review. In a water pistol, a piston drives water through a large tube of area A1 into a smaller tube of area A2 as shown in Figure P14.46. The radius of the large tube is 1.00 cm and that of the small tube is 1.00 mm. The smaller tube is 3.00 cm above the larger tube. (a) If the pistol is fired horizontally at a height of 1.50 m, determine the time interval required for the water to travel from the nozzle to the ground. Neglect air resistance and assume atmospheric pressure is 1.00 atm. (b) If the desired range of the stream is 8.00 m, with what speed v2 must the stream leave the nozzle? (c) At what speed v1 must the plunger be moved to achieve the desired range? (d) What is the pressure at the nozzle? (e) Find the pressure needed in the larger tube. (f) Calculate the force that must be exerted on the trigger to achieve the desired range. (The force that must be exerted is due to pressure over and above atmospheric pressure.)

Figure P14.46

Chapter 14, Problem 14.78AP, Review. In a water pistol, a piston drives water through a large tube of area A1 into a smaller tube

(a)

Expert Solution
Check Mark
To determine

The time required for the water to travel from the nozzle to the ground.

Answer to Problem 14.78AP

The time required for the water to travel from the nozzle to the ground is 0.553s.

Explanation of Solution

The radius of the large tube is 1.00cm and radius of the small tube is 1.00mm. The smaller tube is 3.00cm above the larger tube, the pistol is fired at a height 1.50m with the horizontal.

Formula to calculate the time interval is,

    t=2hg

Here, h is the height of the pistol above the horizontal and g is the acceleration due to gravity.

Substitute 1.50m for h and 9.81m/s2 for g to find t.

    t=2×1.50m9.81m/s2=0.553s

Conclusion:

Therefore, the time required for the water to travel from the nozzle to the ground is 0.553s.

(b)

Expert Solution
Check Mark
To determine

The speed of the stream to leave the nozzle if the range of the stream is 8.00m.

Answer to Problem 14.78AP

The speed of the stream to leave the nozzle is 14.46m/s if the range of the stream is 8.00m.

Explanation of Solution

Formula to calculate the speed of the stream to leave the nozzle is,

    v2=dt

Here, d is the range of the stream and v2 is the speed of the stream to leave the nozzle.

Substitute 8.00m for d and 0.553s for t to find v2.

    v2=8.00m0.553s=14.46m/s

Conclusion:

Therefore, the speed of the stream to leave the nozzle is 14.46m/s if the range of the stream is 8.00m.

(c)

Expert Solution
Check Mark
To determine

The speed of the plunger is moved to achieve the range of 8.00m.

Answer to Problem 14.78AP

The speed of the plunger is 0.1446m/s to achieve the range of 8.00m.

Explanation of Solution

By continuity equation at the plunger and exit point of the nozzle is,

    A1v1=A1v2        (I)

Here, A1 is the area of the large tube, A2 is the area of the smaller tube and v1 is the speed of the plunger.

Formula to calculate the area of the large tube is,

    A1=πr12

Here, r1 is the radius of the large tube.

Formula to calculate the area of the small tube is,

    A2=πr22

Here, r2 is the radius of the small tube.

Substitute πr12 for A1 and πr22 for A2 in equation (I).

`    πr12×v1=πr22×v2v1=r22×v2r12

Substitute 1.00cm for r1, 1.00mm for r2 and 14.46m/s for v2 to find v1.

    v1=(1.00mm×1m1000mm)2×14.46m/s(1.00cm×1m100cm)2=0.1446m/s

Conclusion:

Therefore, the speed of the plunger is 0.1446m/s to achieve the range of 8.00m.

(d)

Expert Solution
Check Mark
To determine

The pressure at the nozzle.

Answer to Problem 14.78AP

The pressure at the nozzle is 101325Pa.

Explanation of Solution

The pressure at the nozzle is equal to the atmospheric pressure.

The atmospheric pressure is equal to the 101325Pa, hence the pressure at the muzzle is equal to the 101325Pa.

Conclusion:

Therefore, the pressure at the nozzle is 101325Pa.

(e)

Expert Solution
Check Mark
To determine

The pressure needed in the large tube.

Answer to Problem 14.78AP

The pressure needed in the large tube is 205860Pa.

Explanation of Solution

Apply the Bernoulli’s equation at point 1 and point 2.

    P1+12ρv12+ρgy1=P2+12ρv22+ρgy2

Here, P1 is the pressure in the large tube, y1 is the elevation at point 1, P2 is the pressure at the exit point of the nozzle, y2 is the elevation at point 2, ρ is the density of the water and g is the acceleration due to gravity.

Substitute 0 for y1, 0.1446m/s for v1, 101325Pa for P2, 14.46m/s for v2, 1000kg/m3 for ρ and 0 for y2 to find P1.

    P1+121000kg/m3×(0.1446m/s)2+ρg(0)=101325Pa+121000kg/m3×(14.46m/s)2+ρg(0)P1=101325Pa+121000kg/m3((14.46m/s)2(0.1446m/s)2)=205860Pa

Conclusion:

Therefore, the pressure needed in the large tube is 205860Pa.

(f)

Expert Solution
Check Mark
To determine

The force exerted on the trigger to achieve the range of 8.00m.

Answer to Problem 14.78AP

The force exerted on the trigger to achieve the range of 8.00m is 35.84N.

Explanation of Solution

Formula to calculate the force exerted on the trigger is,

    F=(P1P2)×A1

Here, F is the force exerted on the trigger.

Substitute πr12 for A1 in the above expression.

    F=(P1P2)×πr12

Substitute 1.00cm for r1, 101325Pa for P2, 205860Pa for P1 to find F.

    F=(205860Pa101325Pa)×π(1.00cm×1m100cm)2=35.84N

Conclusion:

Therefore, the force exerted on the trigger to achieve the range of 8.00m is 35.84N.

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Chapter 14 Solutions

Physics for Scientists and Engineers, Technology Update (No access codes included)

Ch. 14 - A solid iron sphere and a solid lead sphere of the...Ch. 14 - Prob. 14.7OQCh. 14 - One of the predicted problems due to global...Ch. 14 - A boat develops a leak and, after its passengers...Ch. 14 - A small piece of steel is tied to a block of wood....Ch. 14 - A piece of unpainted porous wood barely floats in...Ch. 14 - A person in a boat floating in a small pond throws...Ch. 14 - Rank the buoyant forces exerted on the following...Ch. 14 - A water supply maintains a constant rate of flow...Ch. 14 - A glass of water contains floating ice cubes. When...Ch. 14 - An ideal fluid flows through a horizontal pipe...Ch. 14 - When an object is immersed in a liquid at rest,...Ch. 14 - Two thin-walled drinking glasses having equal base...Ch. 14 - Because atmospheric pressure is about 105 N/m2 and...Ch. 14 - A fish rests on the bottom of a bucket of water...Ch. 14 - You are a passenger on a spacecraft. For your...Ch. 14 - Prob. 14.6CQCh. 14 - Prob. 14.7CQCh. 14 - If you release a ball while inside a freely...Ch. 14 - (a) Is the buoyant force a conservative force? (b)...Ch. 14 - All empty metal soap dish barely floats in water....Ch. 14 - Prob. 14.11CQCh. 14 - Prob. 14.12CQCh. 14 - Prob. 14.13CQCh. 14 - Does a ship float higher in the water of an inland...Ch. 14 - Prob. 14.15CQCh. 14 - Prob. 14.16CQCh. 14 - Prairie dogs ventilate their burrows by building a...Ch. 14 - Prob. 14.18CQCh. 14 - Prob. 14.19CQCh. 14 - A large man sits on a four-legged chair with his...Ch. 14 - Prob. 14.2PCh. 14 - A 50.0-kg woman wearing high-heeled shoes is...Ch. 14 - Estimate the total mass of the Earths atmosphere....Ch. 14 - Calculate the mass of a solid gold rectangular bar...Ch. 14 - (a) A wry powerful vacuum cleaner has a hose 2.86...Ch. 14 - The spring of the pressure gauge shown in Figure...Ch. 14 - The small piston of a hydraulic lift (Fig. P14.8)...Ch. 14 - What must be the contact area between a suction...Ch. 14 - A swimming pool has dimensions 30.0 m 10.0 m and...Ch. 14 - (a) Calculate the absolute pressure at the bottom...Ch. 14 - Prob. 14.12PCh. 14 - Prob. 14.13PCh. 14 - A container is filled to a depth of 20.0 cm with...Ch. 14 - Review. 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The...Ch. 14 - The human brain and spinal cord are immersed in...Ch. 14 - Blaise Pascal duplicated Torricellis barometer...Ch. 14 - Prob. 14.22PCh. 14 - A backyard swimming pool with a circular base of...Ch. 14 - A tank with a flat bottom of area A and vertical...Ch. 14 - A table-tennis ball has a diameter of 3.80 cm and...Ch. 14 - Prob. 14.26PCh. 14 - A 10.0-kg block of metal measuring 12.0 cm by 10.0...Ch. 14 - A light balloon is filled with 400 m3 of helium at...Ch. 14 - A cube of wood having an edge dimension of 20.0 cm...Ch. 14 - The United States possesses the ten largest...Ch. 14 - A plastic sphere floats in water with 50.0% of its...Ch. 14 - A spherical vessel used for deep-sea exploration...Ch. 14 - A wooden block of volume 5.24 104 m3 floats in...Ch. 14 - The weight of a rectangular block of low-density...Ch. 14 - A large weather balloon whose mass is 226 kg is...Ch. 14 - A hydrometer is an instrument used to determine...Ch. 14 - Refer to Problem 16 and Figure P14.16. A...Ch. 14 - On October 21, 2001, Ian Ashpole of the United...Ch. 14 - How many cubic meters of helium are required to...Ch. 14 - Water flowing through a garden hose of diameter...Ch. 14 - A large storage tank, open at the top and filled...Ch. 14 - Prob. 14.42PCh. 14 - Prob. 14.43PCh. 14 - A village maintains a large tank with ail open...Ch. 14 - A legendary Dutch boy saved Holland by plugging a...Ch. 14 - Water falls over a dam of height h with a mass...Ch. 14 - Water is pumped up from the Colorado River to...Ch. 14 - In ideal flow, a liquid of density 850 kg/m3 moves...Ch. 14 - The Venturi tube discussed in Example 14.8 and...Ch. 14 - Review. Old Faithful Geyser in Yellowstone...Ch. 14 - An airplane is cruising al altitude 10 km. The...Ch. 14 - An airplane has a mass of 1.60 104 kg, and each...Ch. 14 - Prob. 14.53PCh. 14 - The Bernoulli effect can have important...Ch. 14 - Prob. 14.55PCh. 14 - Decades ago, it was thought that huge herbivorous...Ch. 14 - (a) Calculate the absolute pressure at an ocean...Ch. 14 - Prob. 14.58APCh. 14 - A spherical aluminum ball of mass 1.26 kg contains...Ch. 14 - Prob. 14.60APCh. 14 - Review. Figure P14.61 shows a valve separating a...Ch. 14 - The true weight of an object can be measured in a...Ch. 14 - Water is forced out of a fire extinguisher by air...Ch. 14 - Review. Assume a certain liquid, with density 1...Ch. 14 - Prob. 14.65APCh. 14 - Prob. 14.66APCh. 14 - Prob. 14.67APCh. 14 - A common parameter that can be used to predict...Ch. 14 - Evangelista Torricelli was the first person to...Ch. 14 - Review. 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