Final answer:
The fractional decrease in pressure when a barometer is raised 40.0 m to the top of a building can be calculated using the concept of hydrostatic pressure.
Step-by-step explanation:
The fractional decrease in pressure when a barometer is raised 40.0 m to the top of a building can be calculated using the concept of hydrostatic pressure. Assuming that the density of air is constant over that distance, we can use the equation for the average pressure due to the weight of a fluid, which is given by:
P_avg = rho * g * h
Where P_avg is the average pressure, rho is the density of air, g is the acceleration due to gravity, and h is the height. In this case, we can substitute the given values:
P_avg = (constant) * 9.8 m/s^2 * 40.0 m = (constant) * 392.0 N/m^2
Thus, the fractional decrease in pressure can be calculated by comparing the pressure at the top of the building to the pressure at the base. Since pressure decreases linearly with height, the formula is:
Fractional decrease = (P_base - P_top) / P_base
Where P_base is the pressure at the base and P_top is the pressure at the top. In this case, P_base can be assumed to be equal to atmospheric pressure, which is roughly 1013.25 hPa. So we have:
Fractional decrease = (1013.25 hPa - (constant) * 392.0 N/m^2) / 1013.25 hPa
This calculation will provide you with the fractional decrease in pressure when the barometer is raised 40.0 m to the top of a building.