Final answer:
To find the angle the string makes with the vertical in a conical pendulum, we can use the relationship between the centripetal force and the tension in the string. The angle the string makes with the vertical is approximately 108.63 degrees. However, none of the given answer options match this value.
Step-by-step explanation:
To find the angle the string makes with the vertical in a conical pendulum, we can use the relationship between the centripetal force and the tension in the string. The centripetal force acting on the bob is provided by the tension in the string and is given by the equation F_c = m * v^2 / r, where F_c is the centripetal force, m is the mass of the bob, v is the speed of the bob, and r is the radius of the circular motion. In this case, m = 1.2 kg, v = 4 m/s, and r = 0.8 m.
Using these values, we can calculate the centripetal force: F_c = (1.2 kg) * (4 m/s)^2 / (0.8 m) = 24 N.
Since the force of gravity (weight) acts downwards, and the tension in the string provides the centripetal force acting towards the center of the circular motion, the angle the string makes with the vertical is the same as the angle between the tension and the vertical. Therefore, we can use trigonometry to find this angle. The tension in the string can be found using the equation T = F_c + mg, where T is the tension, F_c is the centripetal force, m is the mass of the bob, and g is the acceleration due to gravity. In this case, m = 1.2 kg and g = 9.8 m/s^2.
Substituting the values, we get T = 24 N + (1.2 kg) * (9.8 m/s^2) = 35.76 N. Hence, the angle the string makes with the vertical can be found using the equation sin(theta) = T / mg, where theta is the angle. In this case, T = 35.76 N and m = 1.2 kg.
Substituting these values, we get sin(theta) = 35.76 N / (1.2 kg * 9.8 m/s^2) = 3.2197.
Finally, taking the inverse sine of this value, we get theta = arcsin(3.2197) = 1.893 radians. Converting this to degrees, we find theta ≈ 108.63 degrees.
Therefore, the angle the string makes with the vertical is approximately 108.63 degrees. Since none of the answer choices match this value, the correct answer is not provided in the given options.