g A hydraulic press has a safety feature which consists of a hydraulic cylinder with a piston at one end and a safety valve at the other. The cylinder has a radius of 0.0200 m and the safety valve is simply a 0.00750-m radius circular opening at one end, sealed with a disk. The disk is held in place by a spring with a spring constant of 950 N/m that has been compressed 0.0085 m from its natural length. Determine the magnitude of the minimum force that must be exerted on the piston in order to open the safety valve.

58.32 N

Explanation:

Area of a circle =

where r is the radius of the circle.

The cylinder has a radius of 0.02 m, its area is;

=

  = x

  = x 0.0004

  = 1.2571 x

Area of the cylinder is 0.0013 .

The safety valve has a radius of 0.0075 m, its area is;

=

    = x

    = x 5.625 x

    = 1.7679 x

Area of the valve is 0.00018 .

From Hooke's law, the force on the safety valve can be determined by;

F = ke

 = 950 x 0.0085

  = 8.075 N

Minimum force, , required can be determined by;

=

=

=

    = 58.32

The minimum force that must be exerted on the piston is 58.32 N.

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