A conical pendulum swings in a horizontal circle. If the angle of the string with the vertical is θ, what is the relationship between the tension in the string and the gravitational force?
Practice Questions
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Q1
A conical pendulum swings in a horizontal circle. If the angle of the string with the vertical is θ, what is the relationship between the tension in the string and the gravitational force?
T = mg
T = mg/cos(θ)
T = mg/sin(θ)
T = mg/tan(θ)
Tension T provides the centripetal force and balances the weight, T = mg/cos(θ).
Questions & Step-by-step Solutions
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Q
Q: A conical pendulum swings in a horizontal circle. If the angle of the string with the vertical is θ, what is the relationship between the tension in the string and the gravitational force?
Solution: Tension T provides the centripetal force and balances the weight, T = mg/cos(θ).
Steps: 5
Step 1: Understand that a conical pendulum swings in a circle while the string makes an angle θ with the vertical.
Step 2: Identify the forces acting on the pendulum: the tension (T) in the string and the gravitational force (weight, mg) acting downwards.
Step 3: Recognize that the tension in the string has two components: one that balances the weight (mg) and one that provides the centripetal force needed to keep the pendulum moving in a circle.
Step 4: The vertical component of the tension (T * cos(θ)) must balance the weight (mg), so we can write the equation: T * cos(θ) = mg.
Step 5: Rearranging this equation gives us the relationship between tension and gravitational force: T = mg / cos(θ).
