A stone with mass 0.83kg is attached to one end of a string 0.94m long. The string will break if its tension exceeds 62.0N. The stone is whirled in a horizontal circle on a frictionless tabletop; the other end of the string remains fixed. (a) Draw a free body diagram of the stone. (b) Find the maximum speed the stone can attain without the string breaking.
A stone with mass 0.83kg is attached to one end of a string 0.94m long. The string will break if its tension exceeds 62.0N. The stone is whirled in a horizontal circle on a frictionless tabletop; the other end of the string remains fixed. (a) Draw a free body diagram of the stone. (b) Find the maximum speed the stone can attain without the string breaking.
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Transcribed Image Text:**Problem Description:**
A stone with mass 0.83 kg is attached to one end of a string 0.94 m long. The string will break if its tension exceeds 62.0 N. The stone is whirled in a horizontal circle on a frictionless tabletop; the other end of the string remains fixed.
(a) Draw a free body diagram of the stone.
(b) Find the maximum speed the stone can attain without the string breaking.
**Instructions:**
- **Part (a): Free Body Diagram**
- Visualize the stone at the center of a circular path.
- Represent the tension in the string as an arrow pointing radially inward toward the center of the circle.
- Consider gravitational force acting downward and normal force upward, even though their effects are not felt due to the horizontal motion.
- **Part (b): Maximum Speed Calculation**
- Use the formula for centripetal force: \( F = \frac{mv^2}{r} \).
- Set the maximum tension as the centripetal force and solve for \( v \).
- Plug in the given values: \( m = 0.83 \, \text{kg} \), \( r = 0.94 \, \text{m} \), \( F = 62.0 \, \text{N} \).
- Calculate the maximum speed \( v \).
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