In a hidrolic elevator the larger piston have a length of 0.5m.
a) What mass does the car need to have to be lifted by the larger piston if the Force F1 is 200N?
b) Is the smallest piston radius 0.04m?
To answer these questions, we need to use Pascal's Law, which states that the pressure exerted on a fluid is transmitted uniformly in all directions. In a hydraulic system, this principle allows for the amplification of force by applying a small force to a small piston and transmitting it to a larger piston.
a) To find the mass the car needs to have to be lifted by the larger piston, we need to determine the force exerted on the larger piston, given a force of 200N (F1) on the smaller piston. Since pressure (P) is equal to force (F) divided by area (A), we can use this formula to calculate the force exerted on the larger piston.
Let's assume the area of the larger piston (A2) is unknown, and we'll denote it as "x." The area of the smaller piston (A1) is given as 0.04m (the radius squared) since we don't yet know the radius of the smaller piston. We can use the formula F1/A1 = F2/A2 to find the force exerted on the larger piston.
F1/A1 = F2/A2
200N/(π*0.04²m²) = F2/x
Simplifying the equation, we have:
200N/π*0.04²m² = F2/x
To calculate the force exerted on the larger piston (F2), we now solve for x:
F2 = (200N/π*0.04²m²) * x
From here, we can determine the mass (m) needed to create the force F2 using the equation F = mg:
F2 = mg
(200N/π*0.04²m²) * x = m * 9.8m/s²
Therefore, to find the mass (m), we divide both sides of the equation by 9.8m/s²:
m = (200N/π*0.04²m²) * x / 9.8m/s²
b) To determine whether the smallest piston radius is 0.04m, we can compare it to the given radius value. If the given radius matches 0.04m, then the smallest piston radius is indeed 0.04m. If the given radius differs, then the smallest piston radius is not 0.04m.