A cylinder is fitted with a piston, beneath which is a spring, as in the figure. The cylinder is open at the top. Friction is absent. The spring is `3600 N//m`. The piston has a negligible mass and a radius of 0.025m (a) when air beneath the piston is conpletely pumped out, how much does the atmospheric pressure cause the spring to compress? (b) How much work does the atmospheric pressure do in compressing the spring?

Answer

A, B, C, D

Explanation

(a) `p_(0)A=kx`
`:. x=(p_(0)A)/(k) ((p_(0))(pir^(2)))/(k)`
`=((1.0xx10^(5))(pi)(0.025)^(2))/(3600)`
`=0.055m=5.5 cm`.
(b) Work done by atmospheric pressure
`W=(1)/(2)kx^(2)=(1)/(2) (3600)(0.055)^(2)`
`=5.445 J`