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 and the gravitational force acting on the pendulum bob?
Practice Questions
1 question
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 and the gravitational force acting on the pendulum bob?
T = mg
T = mg cos(θ)
T = mg sin(θ)
T = mg tan(θ)
The vertical component of tension balances the weight: T cos(θ) = mg.
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 and the gravitational force acting on the pendulum bob?
Solution: The vertical component of tension balances the weight: T cos(θ) = mg.
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 bob: the tension (T) in the string and the gravitational force (mg) acting downwards.
Step 3: Recognize that the tension 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 forces. The vertical component of the tension (T cos(θ)) must balance the weight of the bob (mg).
Step 5: Write the equation that represents this balance: T cos(θ) = mg.
