Final answer:
To find the radius of the other side of the cylinder when different forces are applied to each side, calculate the input area using the input radius, use Pascal's Law to find the output area, and then find the output radius by taking the square root of the output area divided by pi.
Step-by-step explanation:
To calculate the radius of the other side of a cylinder when force is exerted on its cross-sectional area, you can use Pascal's Law, which states that pressure is transmitted undiminished in an enclosed static fluid. According to this law, the pressure (P) remains constant throughout the fluid, so P = F1/A1 = F2/A2, where F1 and F2 are the input and output forces and A1 and A2 are the cross-sectional areas of the two sides of the cylinder.
Firstly, calculate the area of the input side (A1) using the formula A = πr^2, where r is the radius of the input side. We are given that the radius of the input side is 2.75 m, thus A1 = π(2.75)^2 m2
Then, use Pascal's Law to find the area of the output side (A2) with the output force of 8000.00 N: A2 = F2 * A1 / F1.
Finally, calculate the radius (r2) from the area A2 using the inverse of the area formula: r2 = √(A2/π). Round this radius to three significant figures as requested.
For example, if you were given that the input force (F1) is 5000.00 N and the output force (F2) is 8000.00 N, with the input radius (r1) being 2.75 m, you would carry out the following calculations:
A1 = π(2.75 m)2 = 23.76 m2 (rounded to two decimal places for intermediate steps)
A2 = (8000.00 N * 23.76 m2) / 5000.00 N = 37.82 m2
r2 = √(37.82 m2/π) = 3.47 m (rounded to three significant figures)