1. A U-tube filled with water is closed on one end as shown at right. a. Suppose

Question

1. A U-tube filled with water is closed on one end as shown at right. a. Suppose that the U-tube is about one meter tall. i. Is the pressure at point F greater than, less than, or equal to atmospheric pressure? Explain. On the basis of your answer above, is there a force exerted by the stopper on the water? Explain. ii. The water level on the left is lowered until it reaches point A. H---- The water level in the closed end does not change. Does the pressure at point A increase, decrease, or remain the same? Explain. On the basis of your answer above, does the pressure at point D increase, decrease, or remain the same? Explain. If the pressure changes, how does the change in pressure at point A compare to the change in pressure at point D? Do the pressures at points E and F increase, decrease, or remain the same? How do the changes in pressure at these points compare to the change in pressure at point A? Does the force exerted by the stopper on the top surface of the water increase, decrease or remain the same? Explain. Suppose that point F is 0.5 m above point E. Determine the pressure at point F (in N/m The density of water is p 1000 kg/m g 10 m/s and atmospheric pressure (Hint: What is the pressure at point E?) Tutorials in Introductory Physics CPearson Custom Publishing

Explanation / Answer

part i)

as F and the open end at the left tube are at same height, pressure will be same

so pressure at F is equal to atmospheric pressure.

as pressure on both side of the stopper are equal, there is no force exerted on the stopper.

part ii.

pressure at A earlier was equal to atmospheric pressure+density of water*g*depth of A from the open end

now pressure at A is equal to atmospheric pressure

so pressure at A reduces.

as pressure at D=atmospheric pressure+density of water*g*depth of D from the open end

in the current configuration depth reduces, hence pressure at D reduces.

as depth reduces by same amount for A and D,

decrease in pressure at A=decrease in pressure at D

using similar arguments, pressure at E and pressure at F reduces.

due to pressure mismatch on both sides of the stopper,

there exists a force=pressure difference*surface area

earlier there was no force.

hence force exerted increases.

pressure at E=pressure at A=atmospheric pressure=1.01*10^5 N/m^2

then pressure at F=pressure at E-density of water*g*distance of F from E

=1.01*10^5-1000*10*0.5=96000 N/m^2

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