Final answer:
To analyze a conical pendulum with Newton's Second Law, break down the forces, apply the law to equate the centripetal force with mv²/r, and ensure the solution's reasonableness by considering the forces' components.
Step-by-step explanation:
To analyze the motion of a conical pendulum using Newton's Second Law, we begin by identifying the forces acting on the pendulum. In a conical pendulum, the metal ball moves in a horizontal circle at the end of the string. The centripetal force required for this circular motion is provided by the horizontal component of the tension in the string. The vertical component of the tension must balance the gravitational force acting on the ball.
Newton's Second Law states that the change of motion of a body is proportional to and in the direction of the force acting on it. Applied to the conical pendulum, it means the net force acting towards the center of the circle (centripetal force) is equal to the mass of the ball times the square of its velocity divided by the radius of the circle (F = mv²/r). By breaking down the forces into components and applying Newton's Second Law, we can determine the tension in the string and the speed of the ball.
Lastly, we confirm the reasonableness of our solution. In the case of negligible air resistance and string mass, our calculations should show that the tension in the string has enough horizontal component to provide the required centripetal force and its vertical component should exactly counteract the weight of the ball.