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A hydraulic device consists of a U-shaped tube. The left-hand column is a cylinder 0.5 m in diameter, and the right-hand column is a cylinder 5.0 m in diameter. The entire tub is filled with oil (density 800 kg/m^3). The upper end of each column is covered with a movable piston, which has negligible mass. The entire apparatus is at rest, with both pistons at the same height.
Question 1: What is the area of the left-hand piston? What is the area of the right-hand piston?
Answer: Area = pi*(radius)^2 radius = 0.5*diameter Left-hand piston: Area = pi*(0.25m)^2 = 0.196 m^2 Right-hand piston: Area = pi*(2.5m)^2 = 19.6 m^2
Question 2: Buffalo Bills lineman Ted Washington (mass = 160 kg) steps on the left-hand piston. A Mack Truck (mass = 10000 kg) drives onto the right-hand piston. What is the force exerted by Mr. Washington on the left-hand piston? What is the pressure he places on the piston? What is the force exerted by the truck on the right-hand piston? What is the pressure it places on the piston?
Answer: Force of Mr. Washington = (mass)*(g) = (160 kg)*(9.8 m/s^2) = 1570 N down Pressure of Mr. W on left-hand piston = force/area = (1570 N)/(0.196 m^2) = 8000 N/m^2 Force of truck = (mass)*(g) = (10000 kg)*(9.8 m/s^2) = 98,000 N down Pressure of truck on right-hand piston = force/area = (98,000 N)/(1.96 m^2) = 5000 N/m^2
Question 3: What is the net force on the right-hand piston? Does the Mack truck move up, down, or stay still?
Answer: The force on the left-hand piston is transmitted by the oil to the right-hand piston, and multiplied by the ratio of the piston areas. It is exerted _upwards_ on the right piston, because the oil exerts pressure on the bottom of the piston. area right Force on right piston = (force on left piston)*(----------) area left 19.6 m^2 = (1568 N)*(---------) 0.196 m^2 = (1568 N)*(100) = 156,800 N up Net force on right-hand piston = (force of truck on top) [down] + (force transmitted on bottom) [up] = (98,000 N down) + (156,800 N up) = 58,800 N up So the truck moves up.
This page maintained by Michael Richmond. Last modified Dec 16, 1997.
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