Calculating Ramp Height for Hoop Rolling Up Inclined Angle

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SUMMARY

The discussion focuses on calculating the height a hoop reaches when rolling up a ramp inclined at an angle of 27 degrees, given its center of mass speed of 3.5 m/s at the bottom. The problem is identified as a conservation of energy scenario that involves both translational and rotational motion. The work-energy theorem is applicable, but the confusion arises from visualizing the problem correctly. The hoop rolls without jumping, emphasizing the importance of understanding energy conservation in rotational dynamics.

PREREQUISITES
  • Understanding of conservation of energy principles
  • Familiarity with rotational motion concepts
  • Knowledge of the work-energy theorem
  • Basic trigonometry to analyze inclined planes
NEXT STEPS
  • Study the conservation of energy in rotational dynamics
  • Learn how to apply the work-energy theorem to rolling objects
  • Explore the relationship between linear and angular velocity
  • Investigate the effects of incline angles on rolling motion
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the mechanics of rolling motion and energy conservation principles in inclined planes.

greeenmonke
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A hoop rolls up a ramp inclined at an angle of 27. If the speed of the center of mass of the hoop is 3.5 m/s at the bottom of the ramp, what height will the hoop reach?

I am just not sure how to began. I am thinking i should use work-ene theorem but then i just get stuck. i can't seem to picture the problem. is it a ramp with a hoop moving up the ramp and jumping it? or is rotational problem? I am just confused.
 
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It's a conservation of energy problem with both translation and rotation. The hoop does not jump.
 

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