A salvage yard operator wants to make an electric force linkage for his wrecker crane as a safety device, so that when a vehicle being lifted is too massive, it will break the linkage before the force exerted by the vehicle topples the crane. His plan is to attach two metal plates to the crane cable as shown in Figure P22.9 and connect the plates to the crane's power system. There is to be a positive charge on one plate and a negative charge on the other, so that the two stick together because of the attractive electric force. Discharge is prevented by spraying a layer of plastic on each plate. He needs to know what diameter to make the plates so that they come apart when the vehicle being lifted has a mass greater than \(2000 \mathrm{~kg}\). On the micro level, the electric force is between surface atoms carrying positive charge on one plate and surface atoms carrying negative charge on the other plate. The electric force for each atom pair has a magnitude of \(2.3 \times 10^{-12} \mathrm{~N}\), and each atom occupies an area of \(3 \times 10^{-21} \mathrm{~m}^{2}\).

(a) Before doing any calculations, estimate the necessary plate surface area. Which is this surface area comparable to: that of a pinhead, a fingernail, a music compact disc, a dinner plate, or a manhole cover?

(b) Calculate the necessary area. How accurate was your estimate as to which object the plate area is comparable to?

Data from Figure P22.9

Transcribed Image Text:

positively charged negatively charged to crane