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The piston of a hydraulic elevator used for lifting trucks has a 0.3m radius. What pressure is required to lift a truck of 2500 kg mass? What force was applied to the small piston if it has a radius of 3cm?

Answer :

Answer:

1. 88370.45 N/[tex]m^{2}[/tex]

2. 2500 N.

Explanation:

Pressure, P, is define as the force, F, per unit area, A, applied on/ by an object.

i.e P = [tex]\frac{F}{A}[/tex]

1. The area, A, of the piston of the hydraulic elevator can be determined by;

A = [tex]\pi[/tex][tex]r^{2}[/tex]

where r is the radius of the piston.

A = [tex]\frac{22}{7}[/tex] × [tex](0.3)^{2}[/tex]

  = [tex]\frac{22}{7}[/tex] × 0.09

  = 0.2829 [tex]m^{2}[/tex]

Pressure required to lift a truck of 2500 kg mass can be determined as;

P = [tex]\frac{F}{A}[/tex]

F = W = mg

  = 2500 × 10

  = 25 000 N

So that,

P = [tex]\frac{25000}{0.2829}[/tex]

  = 88370.45 N/[tex]m^{2}[/tex]

The pressure required is 88370.45 N/[tex]m^{2}[/tex].

2. [tex]\frac{F_{1} }{A_{1} }[/tex] = [tex]\frac{F_{2} }{A_{2} }[/tex]

 Area of small piston = [tex]\pi[/tex][tex]r^{2}[/tex]

                                   = [tex]\frac{22}{7}[/tex] × [tex](0.03)^{2}[/tex]

                                   = 0.02829 [tex]m^{2}[/tex]

So that,

[tex]\frac{25000}{0.2829}[/tex] = [tex]\frac{F_{2} }{0.02829}[/tex]

[tex]F_{2}[/tex] = 2500 N

The force applied to the small piston is 2500 N.

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