A force of 625 N is applied to a hydraulic jack piston that is 0.04 m in diameter. If the piston which supports the load has a diameter of 0.60 m, how much mass can be lifted by the jack? Ignore any difference in height between the pistons
To determine how much mass can be lifted by the hydraulic jack, we need to calculate the force exerted by the larger piston (supporting the load).
First, let's find the area of the larger piston using its diameter:
Area = π * (radius)^2
Given that the diameter of the larger piston is 0.60 m, we can calculate the radius as follows:
Radius = diameter / 2 = 0.60 m / 2 = 0.30 m
Now, we can calculate the area:
Area = π * (0.30 m)^2 = 0.09π m^2
Since pressure is the force exerted per unit area, we can use this formula:
Pressure = Force / Area
Rearranging the formula, we have:
Force = Pressure * Area
Given that the force applied to the smaller piston is 625 N, we'll assume that it is equal to the pressure applied to the larger piston:
Force = 625 N
Substituting the values into the formula, we have:
625 N = Pressure * 0.09π m^2
To find the pressure, divide both sides of the equation by 0.09π m^2:
Pressure = 625 N / 0.09π m^2
Pressure ≈ 2207.92 N/m^2
Now that we know the pressure exerted by the hydraulic jack, we can calculate the maximum mass that can be lifted by using the formula:
Force = Mass * Gravity
Rearranging the formula, we get:
Mass = Force / Gravity
Assuming the acceleration due to gravity is approximately 9.8 m/s^2, we can substitute the values into the formula:
Mass = 2207.92 N / 9.8 m/s^2
Mass ≈ 225.13 kg
Therefore, the hydraulic jack can lift a maximum mass of approximately 225.13 kg.