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Describe qualitatively the acceleration acting on a bead that, sliding along a frictionless wire, moves inward with constant speed along a flat spiral.

Describe qualitatively the acceleration acting on a bead that, sliding along a frictionless wire, moves inward with constant speed along a flat spiral.

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
The magnitude of the acceleration of the bead moving in a spiral path centered about a point say P and moving with constant speed v0 is given as:
232-2413_1.PNG
Here r is the magnitude of position vector of the bead relative to point P.
Using the relation above, one can deduce that if the bead slides into the spiral with constant speed, the magnitude of acceleration, which is232-785_1.PNG , increases. To account for this larger acceleration, larger centripetal force must act on the bead. Therefore the acceleration of the bead moving into the spiral will keep of increasing linearly with linear decrease in value of r.

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