 Matt Damon is attempting to improvise an analog local atmospheric pressure sensor on the side of a Martian rover but needs to figure out how big it needs to be. Luckily for him, he knows that the gravity and average atmospheric pressure on Mars are 3.7101 meters per second squared and 610.5 pascals respectively. Calculate the height of the mercury column in a barometer on the Martian surface in millimeters. Remember from thermal 1 that we had come up with an equation, the PAH equation, to relate the pressure change across the height of a column of fluid to that fluid's density, the acceleration it's experiencing, and the height difference between the two points that you're relating with the pressure difference. In this case, the barometer is relating pressure difference between the top of the barometer, which is assumed to have a pressure of about 0 pascals, and atmospheric pressure, and the height difference between these two points is how we determine what that atmospheric pressure is. So we are saying P bottom of the barometer minus P top is equal to the density of this barometer's fluid, which is going to be a mercury column. So we're saying the density of mercury times the acceleration experienced, which is going to be the gravitational acceleration on Mars multiplied by the height of this column, which is what we're actually solving for. P top we know that's 0. P bottom is atmospheric pressure, gravity of Mars we know, and the density of mercury we can look up. For these sorts of lookups, we're going to be using the back of our textbook. The appendices contain, among other things, tables that have physical properties of a variety of fluids. The table that is going to be relevant to us here is table A3. This is going to be properties of common liquids at one atmosphere and 20 degrees Celsius. Now, of course, the mercury on the Martian surface isn't actually at one atmosphere and 20 degrees Celsius, but this is the best property that we have available to us. We don't have mercury tables for Martian atmosphere conditions. So we're going to be assuming that this property is close enough to the density of mercury for the purposes of improvising an atmospheric barometer, and we are using this 13,550 kg per cubic meter density. So from table A3, the density of mercury is about 13,550 kg per cubic meter. At this point, everything in our equation is known except for h. So we can solve for h, that would be P bottom minus P top, which is just P bottom, divided by the density of mercury times gravity. P bottom is the atmospheric pressure, which is 610.5 Pascals. The density we just looked up, 13,550 kg per cubic meter. And the gravitational acceleration on Mars, which is 3.711. We want an answer presumably in millimeters, because the problem asked for that. So I'm going to write 1000 millimeters in one meter. And I'm going to need a little bit more room. I'll scoot this over. And then to get the units inside of the Pascale to cancel, I will break that apart into its component pieces. A Pascale is a Newton per square meter. Newton is a kilogram meter per second squared. So Pascale cancels Pascale. Newton cancels Newton. Meters, meters, meters squared cancels cubic meters and meters, second squared cancels second squared. And kilograms cancels kilograms. That leaves me with just millimeters in the numerator. So by pull up my calculator here, we should be able to coerce it into doing stuff for us. 610.5 multiplied by 1000 divided by 13,550 times 3.711. That's 12.141. So the mercury column required to indicate Martian atmospheric pressure would be rather small. Note that for atmospheric pressure on Earth, it's about 760 millimeters tall. We could come up with that number by using the atmospheric pressure on Earth, about one atmosphere, or 101,325 Pascals instead of 610.5 and a gravitational acceleration of 9.81 instead of 3.711.