Which dam must be stronger, one that holds back 100000 m3 of water 10 m deep or one that holds 1000m3 0f water 20m deep? Why?
They are not asking about exponents here they are asking about which dam is stronger
To determine which dam must be stronger, we need to consider the pressure exerted by the water on the dam. The pressure exerted by a fluid depends on its density and the depth at which it is located.
Pressure (P) = density (ρ) x gravitational acceleration (g) x height (h)
In this case, the density and gravitational acceleration are constant, so we mainly need to compare the heights of the water in the two dams.
For the first dam holding back 100000 m3 of water at a depth of 10 m:
Height (h) = 10 m
For the second dam holding 1000 m3 of water at a depth of 20 m:
Height (h) = 20 m
Based on the formula, we can determine the pressure exerted by each dam. However, it is important to note that the amount of water (volume) being held is not directly proportional to the pressure exerted.
Using the given values, we can calculate the pressure exerted:
For the first dam:
Pressure (P1) = ρ x g x h1
For the second dam:
Pressure (P2) = ρ x g x h2
Since density and gravitational acceleration are the same for both dams, we can compare the heights directly:
P1 = P2 if h1 = h2
However, in this case, h1 (10 m) is less than h2 (20 m). Therefore, the second dam holding 1000 m3 of water at a depth of 20 m will exert higher pressure than the first dam holding 100000 m3 of water at a depth of 10 m.
So, the dam that holds 1000 m3 of water at a depth of 20 m must be stronger to withstand the greater pressure exerted by the deeper water.
Online "^" is used to indicate an exponent, e.g., x^2 = x squared.
100,000 m^3 = 100*1000 m^3