Question

A force of 460 n is exerted on lever ab as shown end b is conected to the piston into a cylinder of diametrer 60 mm what force is required to

Answer 1

Complete question:

A force of 460N is exerted on a level AB as shown. The end B is connected to a piston which fits into a cylinder having a diameter of 60mm. What force FD act on the larger piston if the volume between c and D is filled with water?

Answer:

The force FD is 15835.86 N.

Explanation:

Given,

$F_A = 460 N$

Radius of piston at C ($R_C$) = 60/2 mm = 30 mm

Radius of piston at D ($R_D$) = 260/2 mm = 130 mm

To find,

Force $F_D$

Calculation,

Let the force at B be $F_B$

We apply the torque equation at the hinge

i.e.

$\tau_A = F_A \times 220 mm$ (out of the plane)

$\tau_B = F_B \times 120mm$ (out of the plane)

Now,

$\tau_A = \tau_B\\\implies F_A \times 220 mm = F_B \times 120 mm\\\implies 460 N \times 220 mm = F_B \times 120mm\\\implies F_B = 843.33 N$

Now for finding the force acting at D

$\frac{F_C}{A_C} = \frac{F_D}{A_D}$   (Since, $P_C =P_D$ for equilibrium)

$\frac{F_B}{\pi\times R_C^2} = \frac{F_D}{\pi \times R_D^2}$   (Since, $F_C = F_B$)

$F_D = \frac{F_B \times R_D^2}{R_C^2} \\\implies F_D = \frac{843.33 \times 130^2}{30^2} = 15835.86 N$

Therefore, the force FD is 15835.86 N.

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