A hydraulic lift has a leak so that it is only 6.0 × 101% efficient in raising its load. If the large piston exerts a force of 1.00 × 102 N when the small piston is depressed with a force of 15 N and the radius of the small piston is 18 cm, what is the radius of the large piston?
pressure on each side is the same.
forcesmall*.60/areasmall= forcelarge/arealarge
15/pi*18^2=100/(pi*rl^2*.6)
solve for rlarge.
To solve this problem, we need to use the principle of Pascal's law, which states that the pressure is transmitted equally in all directions in an incompressible fluid. The equation for Pascal's law is:
(P1/A1) = (P2/A2)
Where:
P1 and P2 are the pressures applied on the small and large pistons, respectively.
A1 and A2 are the areas of the small and large pistons, respectively.
We can rearrange this equation to solve for the radius of the large piston (r2):
r2 = √((P1 * A1) / (P2 * π))
First, let's find the area of the small piston (A1). The formula for the area of a circle is:
A = π * r^2
Given the radius of the small piston (r1 = 18 cm), we can find the area:
A1 = π * (r1)^2
Next, we can calculate the pressure applied on the small piston (P1) using the given force:
P1 = F1 / A1
Now, let's calculate the area of the large piston (A2) using the given force (F2 = 100 N) and the efficiency of the hydraulic lift:
F2 = 100% * Efficiency * F1
We can then find the pressure applied on the large piston (P2):
P2 = F2 / A2
Finally, substitute the values into the equation to find the radius of the large piston (r2):
r2 = √((P1 * A1) / (P2 * π))
Now, let's calculate the values and find the radius of the large piston.