A ball is tied to a string and swung in a vertical circle. At the highest point of the circle, what is the condition for the ball to just maintain circular motion?
Practice Questions
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Q1
A ball is tied to a string and swung in a vertical circle. At the highest point of the circle, what is the condition for the ball to just maintain circular motion?
Tension = 0
Tension = mg
Tension > mg
Tension < mg
At the highest point, the centripetal force is provided by the weight, so T + mg = mv²/r, T = 0.
Questions & Step-by-step Solutions
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Q
Q: A ball is tied to a string and swung in a vertical circle. At the highest point of the circle, what is the condition for the ball to just maintain circular motion?
Solution: At the highest point, the centripetal force is provided by the weight, so T + mg = mv²/r, T = 0.
Steps: 8
Step 1: Understand that the ball is moving in a circle and needs a force to keep it moving in that circle.
Step 2: Recognize that at the highest point of the circle, two forces act on the ball: the tension in the string (T) and the weight of the ball (mg).
Step 3: Know that the weight of the ball (mg) acts downwards, while the tension (T) also acts downwards at the highest point.
Step 4: Realize that the total force acting downwards (T + mg) must provide the necessary centripetal force to keep the ball moving in a circle.
Step 5: Write the equation for centripetal force: T + mg = mv²/r, where m is the mass of the ball, v is the velocity, and r is the radius of the circle.
Step 6: For the ball to just maintain circular motion at the highest point, the tension (T) can be zero. This means the weight alone must provide the centripetal force.
Step 7: Substitute T = 0 into the equation: 0 + mg = mv²/r.
Step 8: Simplify the equation to find the condition: mg = mv²/r, which shows that the weight must equal the required centripetal force.
