Video Transcript
A scuba diver dives to a depth of
1.25 metres below the surface of the sea. The seawater has a density of 1025
kilograms per metres cubed. What pressure does the water exert
on the diver to the nearest pascal?
Okay, so in this question, we’re
talking about the sea. So let’s say this is the surface of
the sea. And specifically, we’re talking
about a scuba diver who’s dived to a depth of 1.25 metres below the surface. Now we’ve also been told that the
seawater has a density of 1025 kilograms per metre cubed. What we’ve been asked to do is to
find out the amount of pressure exerted by the water onto the diver to the nearest
pascal.
To do this, we can use the equation
used to find the pressure exerted by a liquid onto an object immersed in that
liquid. The equation in question is that
the pressure exerted by the liquid on the object is equal to the density of the
liquid multiplied by the gravitational field strength of the planet that they’re on,
in this case Earth, multiplied by the depth of that object below the surface of the
liquid.
Now since we’ve been asked to find
out the pressure, we don’t need to rearrange this equation. All we need to do is to sub in the
values. So the pressure exerted on the
diver by the water is equal to the density of the liquid first of all — the liquid
in this case is the water, and we’ve been told this density is 1025 kilograms per
metres cubed — multiplied by the gravitational field strength of Earth, which we can
recall is a constant 9.8 metres per second squared. So we plug that into our
equation. And we also need to multiply it by
the depth of the diver below the surface of the water. That’s 1.25 metres.
Now before we evaluate the
right-hand side of the equation, we also need to remember that we’re working in
standard units. For example, the standard unit of
density is kilograms per metres cubed. So we’ve got this in standard
units. The standard units of gravitational
field strength is metres per second squared. So we’ve also got this in standard
units. And the standard units of depth or
length is metres. So yet again, we’ve got this in
standard units.
What this means is that if all the
quantities on the right-hand side are in their standard units, then the quantities
on the left-hand side, specifically the pressure, will also be in standard units,
which in this case for pressure is pascals. So when we evaluate the right-hand
side, we’ll find the answer in pascals. And actually doing this gives us a
value of 12556.25 pascals.
However, this is not our final
answer. Remember, we’ve been asked to give
our answer to the nearest pascal. So we need to round. Specifically, we need to round this
value here. So we look at the next one, this
two, to see what happens to the six. Now the value after the decimal
point, this two, is less than five. Therefore, our six is not going to
round up. It’s gonna stay the same. And hence, we found our final
answer. The pressure exerted by the water
on the diver to the nearest pascal is 12556 pascals.
