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A hand pump is being used to inflate a bicycle tire that has a gauge pressure of 59.0 lb/in2. If the pump is a cylinder of length 17.4 in. with a cross-sectional area of 3.00 in.2, how far down must the piston be pushed before air will flow into the tire? Assume the temperature is constant.
Answer must be in inches

Respuesta :

Answer:

∴The air cannot be made to flow in with the given pump at the given conditions.

Explanation:

Given:

  • gauge pressure of bicycle tyre, [tex]P_g=59\ lb.in^{-2}[/tex]
  • length of cylinder of the pump, [tex]l=17.4\ in[/tex]
  • area of the the cylinder of the pump, [tex]a= 3\ in^2[/tex]
  • we have the density of air at STP, [tex]\rho=4.4256\times 10^{-5}\ lb.in^{-2}[/tex]

The piston must be pushed more than the pressure inside the tyre:

[tex]P_g=\rho\times V\div a[/tex]

[tex]59=4.4256\times 10^{-5}\times a\times h\div a[/tex]

[tex]h=13.33\times 10^5\ in[/tex]

∴The air cannot be made to flow in with the given pump at the given conditions.

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