Two equal masses of charge 36 nC each are suspended at the end of two 1-m strings of negligible mass.The ropes make and angle of 5 $\circ$ with respect to each other.What is the tension in one of the strings?
A)0.060 N
B)0.044 N
C)0.019 N
D)0.023 N
E)0.035 N

Question

Quizplus · Accepted Answer

To find the tension in one of the strings, we first need to calculate the force of repulsion between the two charges. We can use Coulomb's law for this purpose:$$F = k \frac{q_1 q_2}{r^2}$$where $k = 8.987 \times 10^9 \, \text{N m}^2/\text{C}^2$ is Coulomb's constant, $q_1$ and $q_2$ are the charges (in this case, both are 36 nC or $36 \times 10^{-9}$ C), and $r$ is the distance between the charges.Given that the ropes make an angle of $10^\circ$ with respect to each other, the angle between each rope and the vertical is $5^\circ$. This means the total distance between the charges, $r$, can be found using trigonometry, considering the geometry of the situation where two strings form an isosceles triangle with the charges at the ends. However, the exact distance calculation is not necessary for the choices provided, as we are looking for the tension in the strings, not the distance between charges.The tension in the string has two components due to the equilibrium condition: the vertical component balances the weight of the charge, and the horizontal component balances the electrostatic force of repulsion between the charges.The horizontal component of the tension ($T_{\text{horizontal}}$) is equal to the electrostatic force, and the vertical component ($T_{\text{vertical}}$) supports the weight of the charge. However, without the mass of the charges, we focus on the geometry and the force of repulsion.Given the angle and the charges, we can deduce that the tension in the string is a result of both the gravitational force acting on the mass and the electrostatic repulsion between the charges. However, the exact calculation requires more information than provided (such as the mass of the charges or the distance between them derived from the angle, which was not directly used in the calculation).The correct answer is determined by understanding the balance of forces and the geometry of the situation. However, without explicit calculations shown here due to the error in the angle description and missing steps to directly calculate tension from the given information, we rely on the principle that the tension must counteract both the gravitational pull (which is not directly calculable without mass) and the electrostatic repulsion force. The answer provided assumes familiarity with the principles of equilibrium and electrostatics, but the exact path to the solution involves steps not fully detailed in this response.

Two Equal Masses of Charge 36 NC Each Are Suspended ∘\circ∘

Two Equal Masses of Charge 36 NC Each Are Suspended $\circ$