Please answer all parts of the question The hydraulic system of a mechanical sho

Question

Please answer all parts of the question

The hydraulic system of a mechanical shovel is used to lift a load as shown in the figure. Calculate the force, in newtons, the piston in the slave cylinder must exert to support the 395-kg load and the 145-kg brace and shovel. (b) What is the pressure, in pascals, in the hydraulic fluid if the slave cylinder is 2.6 cm in diameter? (c) What force, in newtons, would you have to exert on a lever with a mechanical advantage of 5.00 acting on a master cylinder 0.81 cm in diameter to create this pressure? (Mechanical advantage of a lever is the factor that the lever increases your applied force).

Explanation / Answer

Here ,

a) let the force due to cylinder is Fc

balancing the moment of forces about the upper support

Fc * 0.30 - 1.1 * sin(30) * 145 * 9.8 - 1.70 * sin(30) * 395 * 9.80 = 0

solving for Fc

Fc = 13573 N

the force of cylinder is 13573 N

b)

pressure , P = FOrce/area

P = 13573/(pi * (0.026/2)^2)

P = 25564615.9 Pa

the pressure inside is 25564615.9 Pa

c)

let the force exerted is F

5F/(pi * (0.81/2)^2) = pressure

5F/(pi * (0.81/2)^2) = 25564615.9

solving for F

F = 2.63 *10^6 N

the force needed is 2.63 *10^6 N

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