The average pressure of the expanding gas.

[{'sectionSequence': 0, 'sectionHeaderText': '', 'solutionSubsections': [{'sectionName': 'To determine', 'sectionText': ' The average pressure of the expanding gas.

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Given data:

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Length of the barrel is 0.61 m.

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Radius of the opening is \r\n2.8×10−3\u2009m\r\n.

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Mass of the bullet is \r\n2.6×10−3\u2009kg\r\n.

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Velocity is \r\n370\u2009ms\r\n.

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Formula used:

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Write the expression of work done.

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W=12mv2\r\n (1)

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Here,

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m\r\n is the mass, and

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v\r\n is the velocity.

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The average pressure is computed by following expression.

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P=WΔV\r\n (2)

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Here,

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ΔV\r\n is the volume of the barrel.

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Calculation:

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Substitute \r\n2.6×10−3\u2009kg\r\n for \r\nm\r\n and \r\n370\u2009ms\r\n for \r\nv\r\n in equation (1),

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W=12(2.6×10−3\u2009kg)(370\u2009ms)2=12×2.6×10−3×136,900\u2009J=177.97\u2009J≅178\u2009J\r\n

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As for the volume of the barrel, the length of the barrel should be multiply with the cross sectional area of the opening that is,

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\u200aΔV=Lπ\u200ar2\r\n (3)

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Here,

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L\r\n is the length of the barrel and

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r\r\n is the radius of the opening

', 'sectionSequence': 2, 'computed': {'sectionNameWithHtmlRemoved': 'Explanation', 'sectionTextWithHtmlRemoved': 'Given data: Length of the barrel is 0.61 m. Radius of the opening is 2.8 × 10 − 3 m . Mass of the bullet is 2.6 × 10 − 3 kg . Velocity is 370 m s . Formula used: Write the expression of work done. W = 1 2 m v 2 (1) Here, m is the mass, and v is the velocity. The average pressure is computed by following expression. P = W Δ V (2) Here, Δ V is the volume of the barrel. Calculation: Substitute 2.6 × 10 − 3 kg for m and 370 m s for v in equation (1), W = 1 2 ( 2.6 × 10 − 3 kg ) ( 370 m s ) 2 = 1 2 × 2.6 × 10 − 3 × 136 , 900 J = 177 .97 J ≅ 178 J As for the volume of the barrel, the length of the barrel should be multiply with the cross sectional area of the opening that is, Δ V = L π r 2 (3) Here, L is the length of the barrel and r is the radius of the opening'}}]}]