A cylinder is fitted with a piston, beneath which is a spring, as in the drawing

Question

A cylinder is fitted with a piston, beneath which is a spring, as in the drawing. The cylinder is open to the air at the top. Friction is absent. The spring constant of the spring is 3564 N/m. The piston has a negligible mass and a radius of 0.033 m.

A cylinder is fitted with a piston, beneath which is a spring, as in the drawing. The cylinder is open to the air at the top. Friction is absent. The spring constant of the spring is 3564 N/m. The piston has a negligible mass and a radius of 0.033 m. When the air beneath the piston is completely pumped out, how much does the atmospheric pressure cause the spring to compress? m How much work does the atmospheric pressure do in compressing the spring?

Explanation / Answer

(a) K * x = force due to atmosphere = 101325 * pi* (0.033)^2

3564*x = 101325 * pi* (0.033)^2

x = 0.097265 m

(b) work =energy stored in the spring = 0.5 * k * x^2 = 0.5 * 3564 * (0.097625)^2 = 16.85858 J

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