A hydraulic press has a ram of 30 cm diameter and a plunger of 4.5 cm diameter. What is the weight lifted by the hydraulic press when the force applied at the plunger is 600 N?a)25.67 kNb)26.67 kNc)28.67 kNd)24.67 kNCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Given:
Ram diameter, D = 30 cm
Plunger diameter, d = 4.5 cm
Force applied, F = 600 N

Formula used:
Pressure P = F/A
Area of ram, A1 = π(D/2)^2
Area of plunger, A2 = π(d/2)^2
Force on ram, F1 = P×A1
Force on plunger, F2 = P×A2

Calculation:
Area of ram, A1 = π(D/2)^2
= π(30/2)^2
= 706.86 cm^2
Area of plunger, A2 = π(d/2)^2
= π(4.5/2)^2
= 15.90 cm^2
Pressure P = F/A2
= 600/15.90
= 37.74 N/cm^2
Force on ram, F1 = P×A1
= 37.74×706.86
= 26726.96 N
Weight lifted by the hydraulic press = F1/1000
= 26.73 kN

Therefore, the weight lifted by the hydraulic press when the force applied at the plunger is 600 N is 26.67 kN (approx).

Answer

26.66

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