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sohan singh singh Grade: 12
        A ring of mass 2.40 kg, inner radius 6.00 cm, and outer radius 8.00 cm rolls (without slipping) up an inclined plane that makes an angle of 36.9°. At the moment the ring is at position x  2.00 m up the plane, its speed is 2.80 m/s. The ring continues up the plane for some additional distance and then rolls back down. It does not roll off the top end. How far up the plane does it go?
7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear Amrit pal


at the given instant total energy of ring is E = 1/2 I w2  + 1/2 mv2


                                                            =1/2 I (V/R)2 + 1/2 mV2


here I =1/2 m (R2 -r2)


E = 1/4 m[1-(r/R)2]V2 + 1/2 mV2


let the ring move L distance in the plane


 increse in potential energy = mgLsin36.9


so from energy balance


1/4 m[1-(r/R)2]V2 + 1/2 mV2   = mgLsin36.9


 


find L from these equation


so total distance move by ring =L+2


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Badiuddin

7 years ago
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