Air spring. The elasticity and bulk modulus of air can be measured using an apparatus co...

Air spring. The elasticity and bulk modulus of air can be measured using an apparatus consisting of a vertical glass tube and a ball bearing that just fits in the inner diameter of the tube. A 110-g ball bearing is dropped into the top of a 47-cm-high glass tube of diameter 3.0 cm. The ball is observed to oscillate as if the air column were a spring, 59 times in 10 s giving a period of 0.17 s. (a) Find the effective spring constant of the air column. (b) Show that this effective spring constant is related to the bulk modulus by where A is the cross-sectional area of the tube and V is the volume of the tube. Hint: Start with Equation 11.25 and express the change in volume in terms of the displacement of the mass. (c) Determine the bulk modulus of air.

(reference equation 11.25)