In a hydraulic system, the area of the large piston is hundred times of the small piston. If 15 N force is applied to the small piston, how much mass can the large piston carry?
In a hydraulic system, the pressure is the same throughout. Therefore, the force applied to the small piston is equal to the force exerted by the large piston. Since the area of the large piston is 100 times that of the small piston, the force exerted by the large piston is 100 times greater than the force applied to the small piston.
So, the force exerted by the large piston is 15 N * 100 = 1500 N.
To find the mass that the large piston can carry, we can use the formula:
Force = mass * gravity
Rearranging the formula, we get:
mass = force / gravity
mass = 1500 N / 9.8 m/s^2
mass ≈ 153.06 kg
Therefore, the large piston can carry approximately 153.06 kg of mass.
To solve this problem, we need to apply Pascal's law, which states that the pressure exerted on a fluid in a closed system is transmitted equally in all directions.
Let's denote the area of the small piston as A1 and the area of the large piston as A2. Given that the area of the large piston is 100 times that of the small piston, we have:
A2 = 100 * A1
The formula for pressure is P = F/A, where P is the pressure, F is the force, and A is the area.
Since the pressure is equal in both pistons, we can set up the equation:
F1/A1 = F2/A2
Substituting the given values:
15 N / A1 = F2 / (100 * A1)
Now we can solve for F2, which is the force exerted on the large piston when a 15 N force is applied to the small piston:
F2 = 15 N * (A2 / A1)
= 15 N * (100 * A1 / A1)
= 15 * 100 N
Therefore, the force exerted on the large piston is 1500 N.
Now, to find the mass the large piston can carry, we can use the equation F = m * g, where F is the force, m is the mass, and g is the acceleration due to gravity.
m = F / g
= 1500 N / 9.8 m/s^2
≈ 153 kg
Therefore, the large piston can carry approximately 153 kg of mass.