Video Transcript
A solid object falls through
water. The water exerts a pressure on the
top, base, and sides of the object. The water pressure on the object is
greatest on its base. Which of the following most
correctly explains why? (A) The object is falling and so is
pushing water below it downward. This water exerts a reaction force
on the base of the object. If the object was suspended in the
water, then the pressure on its base would be equal to the pressure on its other
sides. (B) The pressure due to the weight
of the water acts equally in all directions and increases with depth.
In this question, we are asked to
consider a solid object that is falling through water. We are told that the pressure
exerted on the base of the object is greater than the pressure on the top and
side. Given this, we are asked to figure
out why this is and choose the option that most correctly explains why.
Let’s first recall Pascal’s
principle and figure out how we can apply it to this situation. But Pascal’s principle involves
pressure, so let’s first consider the equation for pressure.
The pressure 𝑃 over an area 𝐴 is
equal to the force 𝐹 divided by that area. Pascal’s principle states that at
any point in a fluid, the pressure exerted by the fluid at that point is equal in
all directions. Also remember that two points in a
fluid that are at the same depth and have no forces acting on them except the weight
of the fluid are at an equal pressure. The pressure they are at increases
with depth; more fluid above the points means more weight exerting pressure on
them.
Now, let’s think about the solid
object from our problem with a top, base, and sides. If we consider the faces of the
object to be a series of points, we can use Pascal’s principle to help solve this
problem.
The points that make up the top of
the object, the side at the shallowest depth, are all at the same height so they all
feel the same force. The points that make up the sides
of the object are at varying heights. And the pressure increases as the
points get closer to the bottom of the object. So, if we were to find the pressure
at each height and add them up, we would see that the sides would experience more
pressure than the top because most of the sides are at a greater depth than the
top.
Now the points that make up the
bottom of the object are all of the same depth, which means they will all experience
the same pressure. The bottom is also at the greatest
depth, which means this side would feel the greatest force.
Looking at option (B), it states
that the pressure due to the weight of the water acts equally in all directions and
increases with depth. This matches what we found using
Pascal’s principle and what we know about the pressure from fluids. So, option (B), the pressure due to
the weight of the water acts equally in all directions and increases with depth, is
the correct answer.
