Piston 1 in the figure has a diameter of 1.87 cm.
Piston 2 has a diameter of 9.46 cm. In the absence of friction, determine the force F, necessary to support an object with a mass of 991 kg placed on piston 2. (Neglect the height difference between the bottom of the two pistons, and assume that the pistons are massless).

Piston 1 in the figure has a diameter of 187 cm Piston 2 has a diameter of 946 cm In the absence of friction determine the force F necessary to support an objec class=

Respuesta :

The force F, necessary to support an object with a mass of 991 kg placed on piston 2 is 379.5 N.

Force necessary to support the object

Apply Pascal principle to calculated the force needed to support the mass as shown below;

F₁/A₁ = F₂/A₂

F₁/d₁² = F₂/d₂²

F₁ = F₂d₁²/d₂²

where;

  • F₂ is the force on piston 2, determined from, F = mg
  • d₂ is the diameter of piston 2, given as 9.46 cm
  • d₁ is diameter of piston 1, given as 1.87 cm
  • F₁ is force on piston 1 = ?

Substitute the given parameters and solve for the  force needed to support the mass given.

F₁ = (991 x 9.8 x 0.0187²)/(0.0946)²

F₁ = 379.5 N

Thus, the force F, necessary to support an object with a mass of 991 kg placed on piston 2 is 379.5 N.

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