Velocity Equal Along Curved Paths?

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SUMMARY

The discussion centers on the comparison of velocities between two bodies falling from the same height: one vertically and the other along a curved path, such as a helix combined with an inclined plane. It is established that if friction is neglected, both bodies will have lost the same amount of potential energy at the same vertical height, leading to the conclusion that their kinetic energies will be equal. Consequently, the velocities at those corresponding points will also be equal, despite the non-uniform acceleration experienced by the body on the curved path.

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  • Understanding of gravitational potential energy and kinetic energy principles
  • Familiarity with the concepts of uniform and non-uniform acceleration
  • Basic knowledge of smooth curved surfaces and their effects on motion
  • Ability to apply energy conservation principles in physics
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  • Study the principles of energy conservation in physics
  • Learn about the effects of friction on motion in curved paths
  • Explore the equations of motion for bodies under non-uniform acceleration
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batballbat
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Lets say a body is falling vertically . Another body is falling along a curved surface maybe like a combination of helix and inclined plane. taking any two corresponding points of the paths, such that the points are at same height from the surface of earth. Or in other words the line joining the points is parallel to horizontal surface. Will the velocity acquired at the two points be equal. Prove it.

Ps. The acceleration of the body in such a curved path won't be uniform. Also neglect friction
 
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If you neglect friction (both air and with the curved surface) then you can apply energy considerations. At the same vertical height both bodies will have lost the same amount of potential energy.
What does this tell you about their kinetic energy?

(I'm assuming the curved surface you refer to is smooth and the object makes contact with it at only one point)
 

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