A treasure chest lies 20.0 m below the surface of the beam. What is the magnitud

Question

A treasure chest lies 20.0 m below the surface of the beam. What is the magnitude of the force that acts on the rectangular top that is 0.750 m times 0.425 m? A) 980 N B) 2.39 times 10^3 N C) 9.48 times 10^4 N D) 4.71 times 10^5 N E) 2.00 times 10^6 N At a location where the acceleration due to gravity is 9.807 times m/s^2, the atmospheric pressure is 9.891 times 10^4 Pa. A barometer at the same location is filled with an unknown liquid. What is the density of the unknown liquid if its height in the barometer is 1.163 m? A) 210 kg/m^3 B) 4336 kg/m^3 C) 5317 kg/m^3 D) 8672 kg/m^3 E) 9688 kg/m^3 A force of 250 N is applied to a hydraulic jack piston that is 0.02 m in diameter. If the piston that supports the load has a diameter of 0.15 m, approximately how much mass can be lifted by the jack? Ignore any difference in height between the pistons. A) 250 kg B) 700 kg C) 1400 kg D) 2800 kg E) 5600 kg Which one of the following statements concerning the buoyant force on an object submerged in a liquid is true? A) The buoyant force depends on the mass of the object. B) The buoyant force depends on the weight of the object. C) The buoyant force is independent of the density of the liquid. D) The buoyant force depends on the volume of the liquid displaced. E) The buoyant force will increase with depth if the liquid is incompressible. A balloon is released from a tall building. The total mass of the balloon including the enclosed gas is 2.0 kg. Its volume is 5.0 m^3. The density of air is 1.3 kg/m^3. Will the balloon rise, fall, or remain stationary; and why? A) The balloon will fall because its density is greater than that of air. B) The balloon will remain stationary because its density is less than that of air. C) The balloon will rise because the upward buoyant force is greater than its weight. D) The balloon will fall because the upward buoyant force is less than its weight. The balloon will fall because the downward buoyant force is greater than the upward buoyant rce.

Explanation / Answer

force = P*A

P = gauge pressure = P0 + rho*g*h = (1.013*10^5) + (1000*9.8*20) = 297300 pa

A = area of cross section = 0.75*0.425

F = 297300*0.75*0.425

F = 9.48*10^4 N

OPTION (C)

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2)

pressure P = rho*g*h

9.891*10^4 = rho*9.807*1.163

density rho = 8672 kg /m^3 <<<<-----answer

OPTION ( D )

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3)

P1 = P2

F1/A1 = F2/A2

F1/(pi*d1^2/4) = F2/(pi*d2^2/4)

d1 = diameter at the force F1 = 250 N

d2 = 0.15 m

F2 = m*g

250/0.02^2 = m*9.81/0.15^2

mass = 1400 kg

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4)

option (D)

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5)

weight of the balloon W = 2*10 = 20 N

buoyancy force Fb = Dair*V*g = 1.3*5*9.8 = 63.7 N

Fnet = Fb - W

Fb > W

Fnet is upwards

OPTION (C)

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