Centripetal force with Conservation of Mass

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SUMMARY

The discussion focuses on calculating the height (h) and speed (v) required for a car to successfully complete a loop in a frictionless environment. The established solutions are h = 5/2 * r and v = √(5gr). Participants emphasize the importance of applying centripetal acceleration principles to derive the necessary speed at the loop's apex.

PREREQUISITES
  • Centripetal acceleration concepts
  • Basic principles of conservation of energy
  • Understanding of gravitational force (g)
  • Familiarity with kinematic equations
NEXT STEPS
  • Study centripetal acceleration calculations in detail
  • Explore conservation of energy in mechanical systems
  • Learn about the effects of friction on motion in loops
  • Investigate real-world applications of circular motion in engineering
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Students studying physics, educators teaching mechanics, and anyone interested in the dynamics of circular motion and energy conservation principles.

nhmockus
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1. Homework Statement : Essentially it is a loop with a ramp leading to it. Find the height h the car would start from in order to complete the loop. Also find the speed the car would have to be at to complete the loop Your answer should be in terms of r. No friction

2. Homework Equations : I know I need to use the equation K(initial) + V(initial)= K(final) + V(final)


3. The Attempt at a Solution : They give us the answers h=5/2*r and v= √5gr but I don't understand how to solve for these
 
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welcome to pf!

hi nhmockus! welcome to pf! :smile:

start by using centripetal acceleration to find the speed needed at the top of the loop :wink:
 

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