What is the formula to find the speed of a ball at he end of a curved ramp?
If I am correct it is just the speed the ball would have if dropped from a vertical height equal to the height difference between the start of the ramp and the end of the ramp. Ignoring friction and air drag of course. If you want to include friction and drag the problem is far more complicated.
Nothing else matters; not the length of the ramp or if it's straight or curved.
For example, if the start of the ramp is at the same height as the end of the ramp then the ball would come to a complete stop just as it reached the end of the ramp. If the end of the ramp is one meter lower than the start of the ramp then the ball's velocity would be the same as if it had been dropped from a height of 1 meter. Again, these two examples only apply if you ignore air drag and friction.
Look up Galileo, he researched all this.
If the ramp is frictionless, the speed of the ball is the same as if it fell from that height. If the ramp is not frictionless and the ball rolls and never slides, then the energy gained equals m g h, but that energy ends up as a combination of angular and linear kinetic energy. In this case you're probably supposed to assume the ball is a solid uniform (same density everywhere) sphere.
Since this seems like homework, you're supposed to show some attempt at solving the problem before more of an answer is provided.
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