A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, the tension in the string is T. What is the expression for T?
Practice Questions
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A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, the tension in the string is T. What is the expression for T?
T = mg
T = mg - mv²/r
T = mg + mv²/r
T = mv²/r
At the highest point, T + mg = mv²/r, thus T = mg - mv²/r.
Questions & Step-by-step Solutions
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Q: A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, the tension in the string is T. What is the expression for T?
Solution: At the highest point, T + mg = mv²/r, thus T = mg - mv²/r.
Steps: 7
Step 1: Understand that the mass m is moving in a vertical circle and at the highest point, there are two forces acting on it: the tension in the string (T) and the weight of the mass (mg).
Step 2: Recognize that at the highest point, both the tension (T) and the weight (mg) contribute to the centripetal force needed to keep the mass moving in a circle.
Step 3: Write down 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 4: Rearrange the equation to solve for the tension (T). Start with T + mg = mv²/r.
Step 5: Subtract mg from both sides to isolate T: T = mv²/r - mg.
Step 6: Factor out m from the right side: T = m(v²/r - g).
Step 7: This gives you the expression for the tension T at the highest point of the circle.
