A salvage yard operator wants to make an electric force linkage for his wrecker

Question

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 1) 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 3300 kg . On the micro level, the electric force is between a surface atom carrying surplus positive charge on one plate and a surface atom carrying surplus negative charge on the other plate. The electric force for each atom pair has a magnitude of 2.3 × 10?12 N, and each atom occupies an area of 3 × 10?21 m2.

Calculate the necessary area.

Explanation / Answer

here

area occupied by each atom , A = 3 * 10^-21 m^2

let the number of atoms be n

effective force of each atom pair, f = 2.3 * 10^-12 N

n * f = m * g

n * 2.3 * 10^-12 = 3300 * 9.8

n = 1.406 * 10^16 atoms

the effective area , a = n * A

a = 1.406 * 10^16 * 3 * 10^-21

a = 4.22 * 10^-5 m^2

the necessary area is 4.22 * 10^-5 m^2

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