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?
Practice Questions
1 question
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
Tension T = mg/cos(θ) to balance the vertical component of weight.
Questions & Step-by-step Solutions
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Q
Q: 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?
Solution: Tension T = mg/cos(θ) to balance the vertical component of weight.
Steps: 6
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).
