To find the radial acceleration of the bob in the conical pendulum, we can use the following formula:
Radial acceleration (ar) = (velocity (v))^2 / radius (r)
To find the velocity, we can use the fact that the pendulum moves in a circle at a constant speed. This means that the magnitude of the velocity is constant.
To find the magnitude of the velocity, we can use trigonometry. The vertical component of the velocity is determined by the component of gravitational force acting along the string, which can be calculated as:
Vertical component of velocity (v_y) = √(2 * g * L * (1 - cos(θ)))
Where g is the acceleration due to gravity (approximately 9.8 m/s^2), L is the length of the string (14.9 cm or 0.149 m), and θ is the angle the string makes with the vertical (6.84°).
Similarly, the horizontal component of the velocity is determined by the component of gravitational force perpendicular to the string, which can be calculated as:
Horizontal component of velocity (v_x) = √(2 * g * L * sin(θ))
Now that we have the magnitude of the velocity, we can calculate the radial acceleration. The radius (r) is the length of the string (L).
Radial acceleration (ar) = (v^2) / r
Substituting the values we have:
Radial acceleration (ar) = ((v_x^2) + (v_y^2)) / L
Finally, to find the horizontal and vertical components of the tension force exerted by the string on the bob, we can use the following formulas:
Horizontal component of tension force (T_x) = m * ar * sin(θ)
Vertical component of tension force (T_y) = m * ar * cos(θ)
Where m is the mass of the bob (0.326 kg), ar is the radial acceleration, and θ is the angle the string makes with the vertical.