A conical pendulum swings with a constant speed. If the angle of the string with
Practice Questions
Q1
A conical pendulum swings with a constant speed. 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 swings with a constant speed. If the angle of the string with the vertical is θ, what is the expression for the tension in the string?
Correct Answer: Tension T = mg/cos(θ)
Step 1: Understand that a conical pendulum swings in a circular motion while the string makes an angle θ with the vertical.
Step 2: Identify the forces acting on the pendulum bob: the weight (mg) acting downwards and the tension (T) in the string acting upwards at an angle.
Step 3: Break down the tension (T) into two components: a vertical component (T * cos(θ)) and a horizontal component (T * sin(θ)).
Step 4: The vertical component of tension (T * cos(θ)) must balance the weight of the bob (mg) to keep it in equilibrium vertically.
Step 5: Set up the equation: T * cos(θ) = mg.
Step 6: Solve for tension (T) by rearranging the equation: T = mg / cos(θ).
Conical Pendulum Dynamics – Understanding the forces acting on a conical pendulum, including tension and gravitational force.
Components of Forces – Breaking down the forces into vertical and horizontal components to analyze motion.
Trigonometric Relationships – Using trigonometric functions to relate the angle of the pendulum to the forces involved.
