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 :

Force necessary to support the object on piston 2 is 24× 10⁴ N.

To find the answer, we need to know about the force and pressure on piston 1 and piston 2.

What's the pressure on piston 2?

  • The force on piston 2= mass × acceleration due to gravity

= 991 Kg × 9.8 = 9414.5N

  • Mathematically, force= pressure/area
  • Pressure= force × area of piston

= 9414.5N × π(9.46² cm² /4)

= 9414.5N × π(9.46²× 10^(-4)m²/4)

= 66.2 N/m²

What's the force needed to held the mass on piston 2?

  • Pressure on piston 2 = pressure on piston 1
  • Force on piston 1= pressure on piston 1/area of piston 1

= 66.2/ π(1.87² cm² /4)

= 66.2/ π(1.87²×10^(-4)m² /4)

= 24× 10⁴ N

Thus, we can conclude that force necessary to support the object on piston 2 is 24× 10⁴ N.

Learn more about the force and pressure here:

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