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 that is of negligible thickness. The sheet is supported by a pole so
that all of its surface is in contact with the liquid apart from a small area that
the pole fits through. The water pushes the sheet when the
container’s movable wall is moved. Which of the following would be the
effect on the sheet of a force 𝐹 pushing the movable wall in the direction shown in
the diagram? (A) The sheet would be pushed
upward as the water pressure below it would increase more than the water pressure
above it. (B) The sheet would not move as the
water pressure above and below it would increase equally. (C) The sheet would be pushed
downward as the water pressure above it would increase more than the water pressure
below it.
Here we are given a figure of water
in a container with a movable wall. In the container, there is a square
metal sheet that is supported by a pole so that all of its surface is in contact
with the water. We are asked to consider what
effects this sheet would experience if the movable wall is pushed with a force 𝐹 in
the direction shown in the diagram.
Recall that this force is related
to the pressure through the following equation. Pressure 𝑃 over an area 𝐴 is
equal to the force acting perpendicularly to the area 𝐹 divided by the area.
To understand what would happen in
this scenario, let’s remind ourselves about Pascal’s principle and how we can apply
it to this problem. Pascal’s principle states that at a
point within a fluid, the pressure of the fluid at that point is equal in all
directions. The question tells us that the
metal sheet is of negligible thickness, so we can say that the top of the sheet and
the bottom of the sheet are at the same height. This means that we can consider our
sheet to be a series of points at the same height within the tank.
Therefore, we can use Pascal’s
principle to say that the pressure acting at each point of the sheet is equal in all
directions, which means that the force pushing down on the sheet is equal to the
force pushing up on the sheet since the sheet has the same area. When the walls move in, the height
of the water above the sheet will increase as the volume of the tank decreases. More water above the sheet leads to
an increase in pressure as the wall moves in. Since the pressure being exerted on
the top and bottom of the sheet are equal to each other, the pressure at all the
points will increase at the same rate.
Looking at the options we are
given, option (B) states that the sheet would not move as the water pressure above
and below it would increase equally. This is what we would expect in
this system due to Pascal’s principle.
So option (B), the sheet would not
move as the water pressure above and below it would increase equally, is the correct
answer.
