Final answer:
The angle that the rod makes with the horizontal can be found by equating the horizontal forces acting on the rod. By solving the equation, we can determine the value of theta, which is approximately 93.06 degrees. Therefore, option D: 9.2° is the correct answer.
Step-by-step explanation:
To find the angle that the rod makes with the horizontal, we need to consider the forces acting on the rod. The weight of the rod acts vertically downward, while the springs provide a force that is perpendicular to the rod. Let's call the angle that the rod makes with the horizontal as theta.
Using the concept of equilibrium, we can analyze the vertical and horizontal forces acting on the rod. The vertical component of the tension in both springs cancels out the weight of the rod, resulting in zero net vertical force. The horizontal components of the tension in both springs add up to provide a net horizontal force. This net force will cause the rod to rotate and make an angle theta with the horizontal.
By equating the horizontal forces, we can solve for theta. The horizontal component of the tension in the first spring is T1*cos(theta), where T1 is the tension in the first spring and theta is the angle that the rod makes with the horizontal. Similarly, the horizontal component of the tension in the second spring is T2*cos(theta). Since the net horizontal force acting on the rod is zero, we have T1*cos(theta) + T2*cos(theta) = 0.
Substituting the values of the spring constants, we get (47 N/m)*(0.80 m)*cos(theta) + (35 N/m)*(0.80 m)*cos(theta) = 0. Solving this equation gives us cos(theta) = -0.074. Taking the inverse cosine, we find that theta is approximately 93.06 degrees.
Therefore, the angle that the rod makes with the horizontal is approximately 93.06 degrees, which is close to option D: 9.2°.