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26 September, 20:15

A hydraulic press has one piston of diameter 2.0 cm and the other piston of diameter 16.0 cm. What force must be applied to the smaller piston to obtain a force of 3200 N at the larger piston?

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  1. 26 September, 20:41
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    The force applied to the smaller piston = 2512 N

    Explanation:

    Hydraulic press: A hydraulic press is a device used to produce a very large force. A hydraulic force operates based on pascal's principle.

    F/f = A/a ... Equation 1

    making f the subject of the equation above

    f = (F*a) / A ... Equation 2

    Where F = Force on the larger piston, f = force on the smaller piston, A = area of the larger piston, a = area of the smaller piston.

    Given: F = 3200 N, and

    Area (A) = πD²/4 where D = 16.0 cm = 0.16 m

    A = 3.143 * (0.16) ²/4 = 0.02 m²

    Also

    a = πd²/4 where d = 2 cm = 0.02 cm

    a = 3.143 * (0.02) ²/4

    a = 0.0157 m²

    Substituting these values into equation 2

    f = (3200*0.0157) / 0.02

    f = 2512 N

    The force applied to the smaller piston = 2512 N
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