A conical pendulum 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
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 expression for the tension in the string?
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, thus 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 expression for the tension in the string?
Solution: The vertical component of tension balances the weight: T cos(θ) = mg, thus T = mg/cos(θ).
Steps: 6
Step 1: Understand that a conical pendulum swings in a horizontal circle, meaning it has both vertical and horizontal components of motion.
Step 2: Identify the forces acting on the pendulum. The two main forces are the tension in the string (T) and the weight of the pendulum (mg), where m is mass and g is the acceleration due to gravity.
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: Focus on the vertical component of the tension. This component must balance the weight of the pendulum, which is mg. Therefore, we can write the equation: T cos(θ) = mg.
Step 5: To find the tension (T), rearrange the equation from Step 4. Divide both sides by cos(θ): T = mg / cos(θ).
Step 6: This final expression T = mg / cos(θ) gives us the tension in the string of the conical pendulum.
