Chapter 25, Problem 45AP

You are part of a team working in a machine parts mechanic’s shop. An important customer has asked your company to provide springs with a very precise force constant k. You dense the electrical circuit shown in Figure P25.45 to measure the spring constant of each of the springs to be provided to the customer. The circuit consists of two identical, parallel metal plates free to move, other than being connected to identical metal springs, a switch, and a battery with terminal voltage ΔV. With the switch open, the plates are uncharged, are separated by a distance d, and have a capacitance C. When the switch is closed, the plates become charged and attract each other. The distance between the plates changes by a factor f, after which the plates are in equilibrium between the spring forces and the attractive electric force between the plates. To keep the plates from going into oscillations, you hold each plate with insulating gloves as the switch is closed and apply a force on the plates that allows them to move together at a slow constant speed until they are at the equilibrium separation, at which point you can release the plates. You determine an expression for the spring constant in terms of C, d, ΔV, and f.

Figure P25.45 Problems 45 and 50.