A conical pendulum consists of a mass m attached to a string of length L, swingi
Practice Questions
Q1
A conical pendulum consists of a mass m attached to a string of length L, swinging in a horizontal circle. What is the expression for the tension in the string?
T = mg
T = mg/cos(θ)
T = mg/sin(θ)
T = m(v²/r)
Questions & Step-by-Step Solutions
A conical pendulum consists of a mass m attached to a string of length L, swinging in a horizontal circle. What is the expression for the tension in the string?
Correct Answer: T = mg/cos(θ)
Step 1: Understand the setup of a conical pendulum. It consists of a mass (m) attached to a string of length (L) that swings in a horizontal circle.
Step 2: Identify the forces acting on the mass. There are two main forces: the gravitational force (mg) acting downwards and the tension (T) in the string acting along the string.
Step 3: Recognize that the string makes an angle (θ) with the vertical. This angle is important for calculating the components of the forces.
Step 4: Break down the tension (T) into two components: a vertical component (T * cos(θ)) that balances the weight (mg) and a horizontal component (T * sin(θ)) that provides the centripetal force for circular motion.
Step 5: Set up the equation for the vertical forces. Since the mass is in equilibrium vertically, we have T * cos(θ) = mg.
Step 6: Solve for the tension (T). Rearranging the equation gives T = mg / cos(θ).
Step 7: Conclude that the expression for the tension in the string of a conical pendulum is T = mg / cos(θ).
Conical Pendulum Dynamics – Understanding the forces acting on a mass in circular motion, including tension, gravitational force, and the angle of the string.
Centripetal Force – Recognizing that the tension in the string provides the necessary centripetal force for circular motion.
Trigonometric Relationships – Applying trigonometric functions to relate the angle of the pendulum to the forces acting on the mass.
