A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, what is the condition for the mass to just complete the circular motion?
Practice Questions
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Q1
A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, what is the condition for the mass to just complete the circular motion?
Tension = 0
Tension = mg
Tension = 2mg
Tension = mg/2
At the highest point, the centripetal force is provided by the weight of the mass, so T + mg = mv²/r. For T = 0, mg = mv²/r.
Questions & Step-by-step Solutions
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Q
Q: A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, what is the condition for the mass to just complete the circular motion?
Solution: At the highest point, the centripetal force is provided by the weight of the mass, so T + mg = mv²/r. For T = 0, mg = mv²/r.
Steps: 8
Step 1: Understand that the mass m is moving in a vertical circle attached to a string.
Step 2: Identify the highest point of the circle where the mass is located.
Step 3: Recognize that at the highest point, two forces act on the mass: the weight of the mass (mg) acting downwards and the tension in the string (T) also acting downwards.
Step 4: Know that for the mass to stay in circular motion, there must be a net inward force (centripetal force) towards the center of the circle.
Step 5: Write the equation for centripetal force at the highest point: T + mg = mv²/r, where v is the speed of the mass and r is the radius of the circle.
Step 6: To find the condition for the mass to just complete the circular motion, consider the case where the tension T is zero (T = 0). This means the weight of the mass must provide all the necessary 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 can be rearranged to v² = g * r.
