1) Estimate the total hydrostatic force ? on the Hoover Dam.
2)A 0.550 kg metal cylinder is placed inside the top of a plastic tube, the lower end of which is sealed off by an adjustable plunger. The cylinder comes to rest some distance above the plunger. The plastic tube has an inner radius of 5.54 mm and is frictionless. Neither the plunger nor the metal cylinder allow any air to flow around them. If the plunger is suddenly pushed upwards, increasing the pressure between the plunger and the metal cylinder by a factor of 1.83 , what is the initial acceleration ? of the metal cylinder? Assume the pressure outside of the tube is 1.00 atm .
2)
Po = pressure outside the tube = 1 atm = 101325 Pa
r = radius = 5.54 mm = 5.54 x 10-3 m
m = mass of cylinder = 0.550 kg
Area is given as
A = r2 =
(3.14)(5.54 x 10-3)2 = 9.64 x 10-5
m2
initial pressure is given as
P = Po + (mg/A)
P = 101325 + (0.550 x 9.8/( 9.64 x 10-5))
P = 1.57 x 105 Pa
new pressure after the plunger move is given as
P' = 1.83 P
P' = 1.83 x 1.57 x 105
P' = 2.87 x 105 Pa
force equation for the motion is given as
(P' - Po) A - mg = ma
(2.87 x 105 - 101325) (9.64 x 10-5) - (0.550) (9.8) = (0.550) a
a = 22.74 m/s2
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