Four non-conducting wires each with mass m = 1 kg and length ℓ = 2.0 m...
Analysis of the Square's Motion
Performing Oscillatory Motion:- Yes, the square will perform oscillatory motion due to the electric forces acting on each wire.
Performing Simple Harmonic Motion (SHM):- The square will perform SHM as the restoring force acting on each wire is proportional to the displacement from the equilibrium position.
Maximum Angular Speed:- The maximum angular speed can be calculated using the equation for SHM: ω = sqrt(k/m), where k is the force constant and m is the mass of each wire.
- The force constant k can be calculated as the product of the charge per unit length and the electric field strength.
Explanation:
Oscillatory Motion:- The electric forces acting on each wire will cause the square to rotate about its center, leading to oscillatory motion.
Simple Harmonic Motion (SHM):- The restoring force acting on each wire is directly proportional to the displacement from the equilibrium position, leading to SHM.
Maximum Angular Speed Calculation:- The force constant k is given by k = (charge per unit length) * E = 1 * 4 = 4 N/m.
- Substituting k = 4 N/m and m = 1 kg into ω = sqrt(k/m), we get ω = sqrt(4/1) = 2 rad/s.