how to get

Question

The data below refers to a single acting hydraulic jack used in a service station: Diameter of ram cylinder= 510 mm Stroke length of the plunger= 100 mm Diameter of the plunger= 60 mm Mechanical advantage of the lever= 25 Calculate the effort that must be applied to the lever to lift an engine of ONE ton Calculate the number of strokes needed by the plunger to lift the load by 410 mm, if there is a slip of 9%

Answer 1

Given

Mass of the load, m = 1 ton = 907.2 kg

Diameter of ram cylinder, D_C = 510 mm

Stroke length of the plunger,S= 100 mm

Diameter of the plunger,D_P= 60 mm

Mechanical advantage of the lever,MA= 25

Calculate the weight of the load.

W = mg

    = (907.2)(9.81) =8900 N

Calculate the pressure .

P = W/A_C

    = W/(π/4)(D_C )²

     =8900/(π/4)(510 )²

     = 0.0436 N/mm²

Calculate the acting force on the plunger.

F = PA_P

   = P(π/4)(D_P )²

    = 0.0436(π/4)(60 )²

    = 123.2 N

Calculate the input force.

F_in =F/MA

       =123.2/25

       = 4.927 N

Therefore, the effort is 4.927 N

Answer 2

Calculate displacement volume per stroke.

V _P  = (A _P )(Stroke length) =(π/4)(D_P )²(Stroke length)

       =(π/4)(60 )²(100)

         =282735 mm³ /stroke

Corrrected volume per stroke.

V correct =(1-(9/100))V _P    (Since there is a 9% slip)

                 =(1-(9/100))(282735)

                 = 257288 .85 mm³ /stroke

Calculate displacement volume for ram.

Vram =ram area × ram displacement = (π/4)(D_C )²× ram displacement

           =(π/4)(510 )²(410)

         = 83789357.143 mm³

Calculate the number of strokes

stroke =Vram/V correct

          =83789357.143/257288 .85

          =325.66 strokes

Therefore, number of strokes are 326 strokes