Block moving on a frictionless loop

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SUMMARY

The discussion centers on determining the minimum height from which a block must be released on a frictionless slide to complete a vertical loop without losing contact with the surface. Key concepts include the necessity of a minimum speed at the top of the loop to counteract gravitational force. The block must maintain sufficient centripetal acceleration to remain in contact, which is derived from the gravitational force acting on it. The analysis emphasizes the relationship between potential energy at the release height and kinetic energy required at the loop's apex.

PREREQUISITES
  • Understanding of gravitational force and centripetal acceleration
  • Familiarity with energy conservation principles
  • Basic knowledge of circular motion dynamics
  • Ability to apply Newton's laws of motion
NEXT STEPS
  • Study the principles of energy conservation in mechanical systems
  • Learn about centripetal force requirements for circular motion
  • Explore the dynamics of roller coasters and similar systems
  • Investigate the mathematical derivation of minimum speed at the top of a loop
USEFUL FOR

Physics students, educators, and anyone interested in understanding the mechanics of motion on curved paths, particularly in scenarios involving loops and gravitational forces.

phosgene
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Homework Statement



A block moves on the frictionless slide shown in the diagram. What is the minimum height from which the block can be released if it is to complete the loop without leaving the surface of the slide? (Assume that the dimensions of the block are small compared to R, and that there is no energy associated with rotational motion of the block.) Hint: Think about the minimum speed of the block at the top of the loop if it is to remain in contact with the surface.

physicsdiagram-1.png


Homework Equations



?

The Attempt at a Solution



I have no idea at all! I mean, for the block to stay in contact with the top of the loop, it would need some kind of force to counteract gravity. Even if it was moving really fast, wouldn't the slightest influence of gravity pull it away from the loop? But I can't think of any force acting against gravity. Well, I'm pretty sure that this reasoning is wrong, because I've seen something like this done in real life. So I'm totally stuck..
 
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haven't you ever seen a rollercoaster go around a loopdeloop? Or swinging water over your head in a bucket and it not coming out? What force is applied to something that is moving in a circle?
 
phosgene said:
But I can't think of any force acting against gravity.
There does not necessarily have to be a force acting against gravity at the top of the loop if the object is accelerating vertically downward at that point. Is it?
 

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