Calculate the force exerted by the ram piston of a hydraulic press if an effort of 200 N is applied to the end of the lever that operates the plunger. The mechanical advantage of the lever system is 10 and the efficiency of the press is 85%. The diameter of the plunger is 25 mm and that of the ram piston is 200 mm.
First, we need to calculate the force exerted by the lever system:
Effort (E) = 200 N
Mechanical Advantage (MA) = 10
Output Force = Effort x Mechanical Advantage
Output Force = 200 N x 10
Output Force = 2000 N
Next, we need to calculate the force exerted by the ram piston. We know that the force exerted by the ram piston is equal to the force exerted by the plunger with the same cross-sectional area.
Area of plunger (A1) = π(r1)^2
r1 = 25 mm / 2 = 12.5 mm = 0.0125 m
A1 = π(0.0125)^2
A1 = 0.00049087 m^2
Area of ram piston (A2) = π(r2)^2
r2 = 200 mm / 2 = 100 mm = 0.1 m
A2 = π(0.1)^2
A2 = 0.03142 m^2
Force exerted by the plunger (F1) = Pressure x Area
Force exerted by the ram piston (F2) = Pressure x Area
Since the pressure is the same in both cases, we can equate the two to find the force exerted by the ram piston in terms of the force exerted by the lever system:
F1 = F2
Pressure x A1 = Pressure x A2
F2 = F1 x (A2 / A1)
F2 = 2000 N x (0.03142 m^2 / 0.00049087 m^2)
F2 = 2000 N x 64.017
F2 = 128034 N
However, the efficiency of the press is 85%, so we need to consider that:
Actual force exerted by the ram piston = Force exerted by the ram piston / Efficiency
Actual force exerted by the ram piston = 128034 N / 0.85
Actual force exerted by the ram piston = 150040 N
Therefore, the force exerted by the ram piston of the hydraulic press is approximately 150040 N.