A conical pendulum consists of a mass attached to a string that swings in a hori
Practice Questions
Q1
A conical pendulum consists of a mass attached to a string that swings in a horizontal circle. If the angle of the string with the vertical is θ, what is the expression for the tension in the string?
mg/cos(θ)
mg/sin(θ)
mg/tan(θ)
mg
Questions & Step-by-Step Solutions
A conical pendulum consists of a mass attached to a string that swings in a horizontal circle. If the angle of the string with the vertical is θ, what is the expression for the tension in the string?
Step 1: Understand that a conical pendulum has a mass (m) attached to a string that swings in a horizontal circle.
Step 2: Identify the angle (θ) that the string makes with the vertical.
Step 3: Recognize that the weight of the mass (mg) acts downward due to gravity.
Step 4: The tension (T) in the string has two components: a vertical component and a horizontal component.
Step 5: The vertical component of the tension (T) must balance the weight of the mass (mg). This can be expressed as T * cos(θ) = mg.
Step 6: To find the tension (T), rearrange the equation: T = mg / cos(θ).
Step 7: This equation shows how the tension in the string relates to the weight of the mass and the angle θ.
Conical Pendulum Dynamics – Understanding the forces acting on a mass in a conical pendulum, including tension and gravitational force.
Components of Forces – Breaking down the tension in the string into vertical and horizontal components to analyze motion.
Trigonometric Relationships – Using trigonometric functions to relate the angle of the string to the forces acting on the mass.
