A conical pendulum swings in a horizontal circle. If the angle of the string wit

Practice Questions

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 acting on the pendulum bob?

T = mg
T = mg cos(θ)
T = mg sin(θ)
T = mg tan(θ)

Questions & Step-by-Step Solutions

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 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: The vertical component of the tension (T cos(θ)) must balance the weight of the pendulum bob (mg) because there is no vertical motion.
Step 5: Write the equation that represents this balance: T cos(θ) = mg.

Forces in a Conical Pendulum – The relationship between tension and gravitational force in a conical pendulum involves resolving forces into vertical and horizontal components.
Trigonometric Relationships – Understanding how to apply trigonometric functions (cosine) to relate the angle of the pendulum to the forces acting on it.

A conical pendulum swings in a horizontal circle. If the angle of the string wit

Practice Questions

Questions & Step-by-Step Solutions

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