A conical pendulum consists of a mass attached to a string that 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?
Practice Questions
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Q1
A conical pendulum consists of a mass attached to a string that 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?
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 consists of a mass attached to a string that 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?
Solution: Tension T = mg/cos(θ) to balance the vertical component of weight.
Steps: 7
Step 1: Understand that a conical pendulum has a mass (m) attached to a string that swings in a horizontal circle.
Step 2: Identify the angle (θ) that the string makes with the vertical.
Step 3: Recognize that the weight of the mass (mg) acts downward due to gravity.
Step 4: The tension (T) in the string has two components: a vertical component and a horizontal component.
Step 5: The vertical component of the tension (T) must balance the weight of the mass (mg). This can be expressed as T * cos(θ) = mg.
Step 6: To find the tension (T), rearrange the equation: T = mg / cos(θ).
Step 7: This equation shows how the tension in the string relates to the weight of the mass and the angle θ.
