A conical pendulum swings in a horizontal circle. If the angle of the string wit
Practice Questions
Q1
A conical pendulum 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?
T = mg
T = mg/cos(θ)
T = mg/sin(θ)
T = mg tan(θ)
Questions & Step-by-Step Solutions
A conical pendulum 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 swings in a horizontal circle, meaning it has both vertical and horizontal components of motion.
Step 2: Identify the forces acting on the pendulum. The two main forces are the tension in the string (T) and the weight of the pendulum (mg), where m is mass and g is the acceleration due to gravity.
Step 3: Recognize that the tension in the string can be broken down into two components: a vertical component (T cos(θ)) and a horizontal component (T sin(θ)).
Step 4: Focus on the vertical component of the tension. This component must balance the weight of the pendulum, which is mg. Therefore, we can write the equation: T cos(θ) = mg.
Step 5: To find the tension (T), rearrange the equation from Step 4. Divide both sides by cos(θ): T = mg / cos(θ).
Step 6: This final expression T = mg / cos(θ) gives us the tension in the string of the conical pendulum.
Conical Pendulum Dynamics – Understanding the forces acting on a conical pendulum, including tension and gravitational force.
Components of Forces – Breaking down the tension force into vertical and horizontal components to analyze motion.
Trigonometric Relationships – Using trigonometric functions to relate the angle of the pendulum to the forces involved.
