Video Transcript
Water in a container is pushed
horizontally by a movable wall of the container, as shown in the diagram. Within the water in the container
is a square metal sheet. The base of the sheet is attached
to the floor of the container, keeping the sheet vertically oriented. The water pushes the sheet when the
container’s movable wall is moved. When a force 𝐹 pushes the movable
wall in the direction shown in the diagram, how does the change in water pressure on
the side of the sheet facing the movable wall compare to the change in the water
pressure on the side of the sheet facing in the opposite direction to the movable
wall? (A) The water pressure on each face
of the sheet changes equally. (B) The water pressure on the face
of the sheet facing the movable wall increases more than the water pressure on the
opposite face of the sheet. (C) The water pressure on the face
of the sheet facing the movable wall increases less than the water pressure on the
opposite face of the sheet.
In this question, we are shown a
figure of a tank filled with water and with one movable wall. Inside the water, there is a sheet
that is standing vertically, as shown in the figure, with the base of this sheet
attached to the bottom of the tank. We are asked to figure out what
would happen to the pressure on either side of the sheet when a force, 𝐹, pushes on
the movable wall, making the part of the tank holding the water smaller.
Let’s remind ourselves of some
information about how fluids exert pressure and then try to figure out what would
happen in this scenario. First, recall Pascal’s
principle. Pascal’s principle states that at a
point in a fluid, the pressure exerted by the fluid at that point will be equal in
every direction. Another important fact to remember
is that the pressure exerted at two points at the same depth are equal. This means that the pressure
exerted by a fluid is uniform on planes parallel to the surface and the pressure
depends purely on the depth we are measuring at.
It is also helpful to remember that
the pressure 𝑃 exerted over an area 𝐴 is equal to the force exerted 𝐹 divided by
that area. The force in this case is due to
the weight of the fluid above the point we are measuring at. Now, let’s take a look at the
scenario we were given again and figure out what will happen. As the movable wall is pushed with
the force 𝐹, the volume containing the water decreases and causes the height of the
water to increase, as the only space available is above it. This in turn will cause the
pressure on the plate to increase because there will be a larger column of water
directly above it.
This question is asking us to
compare this increase in pressure on either side of the plate. If we apply the principles we know
about the pressure exerted by fluids, we can figure this out. We know that two points at the same
depth in a fluid will experience the same pressure. We can also see that either side of
the plate is at the same height because it is oriented vertically with the base
attached to the bottom of the tank. The pressure each side will feel
will be equal, which means that as the wall moves, the pressure on either side will
remain equal by increasing at the same rate. This is because as the wall moves,
only the height of the water’s surface changes, increasing the depth of the
sheet.
Therefore, option (A), the water
pressure on each face of the sheet changes equally, is the correct answer.
