Circular Motion of a moving rock Problem

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SUMMARY

The problem involves calculating the minimum speed required for a 480g rock to remain in contact with the bottom of a bucket while swinging in a vertical circle with a diameter of 2.8m. The correct approach uses the equation N + mg = mv²/r, where N is the normal force, m is mass, g is acceleration due to gravity (9.8 m/s²), and r is the radius (1.4m). The correct minimum speed at the top of the circle is determined to be 5.2 m/s, but the initial calculation was incorrect due to using the diameter instead of the radius.

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  • Understanding of circular motion dynamics
  • Familiarity with Newton's laws of motion
  • Knowledge of gravitational force calculations
  • Ability to manipulate algebraic equations
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  • Review the principles of circular motion and centripetal force
  • Study the effects of normal force in vertical circular motion
  • Learn about the role of radius in circular motion calculations
  • Practice solving similar problems involving forces in circular motion
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Homework Statement


You hold a bucket in one hand. In the bucket is a 480g rock. You swing the bucket so the rock moves in a vertical circle 2.8m in diameter. What is the minimum speed the rock must have at the top of the circle if it is to always stay in contact with the bottom of the bucket?

Homework Equations


N + mg = mv^2/r

The Attempt at a Solution


I thought this was going to be a simple answer. So I set N = 0, because that is the when the rock is about to lose contact. So then I solved for v = sqrt(r*g), which is sqrt(9.8*2.8) which gave me 5.2 m/s, but it is saying it is wrong? I think my problem must be than N must be something other than 0? But I'm not sure what to put N as in that case. Can someone help me?
 
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N is 0 for sure, but you used the diameter instead of the radius!
 
Well, damn. Thanks mate haha.
 

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