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A potato gun having a 0.560 m long barrel fires a 300 g potato by means of expanding gas. As the gas expands, the force on the potato is Fx = 14,500 N + (9000 N/m)x − (25,000 N/m2)x2, where x is in meters the x axis is along the lenght of the barrel. Determine the work done by the gas on the potato as it travels the length of the barrel.

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The work done by the gas on the potato as it travels the length of the barrel is 6,552 J.

The given parameters;

  • Length of the potato gun, x = 0.56 m
  • Mass of the barrel, m = 300 g = 0.3 kg
  • The force on the potato, [tex]F_x = 14,500 \ N + (9000\ N/m)x - (25,000\ N/m^2)x^2[/tex]

The force on the potato along the barrel is calculated as follows;

F = (14,500) + (9,000 x 0.56) - (25,000 x 0.56 x 0.56)

F = 11,700 N

The work done by the gas on the potato as it travels the length of the barrel is calculated as follows;

Work-done = force x distance

Work-done = 11,700 x 0.56

Work-done = 6,552 J.

Thus, the work done by the gas on the potato as it travels the length of the barrel is 6,552 J.

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