Two small metal cubes with masses 2.0 g and 4.0 g are tied together by a 5.0-cm-long massless string and are at rest on a frictionless surface. Each is charged to +2.0 μC.
b. What is the tension in the string?
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1
Identify the charges on each cube and recognize that they are identical and positive, which means they will repel each other.
Use Coulomb's Law to calculate the electrostatic force (F) between the two charges. Coulomb's Law is given by F = k \frac{q_1 q_2}{r^2}, where k is Coulomb's constant (approximately 8.99 \times 10^9 N m^2/C^2), q_1 and q_2 are the charges on the cubes, and r is the distance between the centers of the cubes.
Since the string is massless and the surface is frictionless, the only force acting along the string is the electrostatic force, which is also the tension in the string.
Substitute the values into the Coulomb's Law equation: q_1 = q_2 = +2.0 \mu C (which needs to be converted to coulombs, where 1 \mu C = 10^{-6} C) and r = 5.0 cm (which needs to be converted to meters, where 1 cm = 0.01 m).
Calculate the tension in the string using the modified Coulomb's Law equation with the substituted values.