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# Quick M3 question watch

1. A bead B of mass 0.8kg is threaded on a smooth circular wire centre O and radius 0.4m which is fixed in a horizontal plane. A light inextensible string is attached to B and passes through a small smooth horizontal ring at O and carries a mass of 0.4kg which is hanging freely. B is moving on the wire with a constant speed of 5m/s. Calculate the magnitude and direction of the reaction of the wire on B.
2. (Original post by Widowmaker)
A bead B of mass 0.8kg is threaded on a smooth circular wire centre O and radius 0.4m which is fixed in a horizontal plane. A light inextensible string is attached to B and passes through a small smooth horizontal ring at O and carries a mass of 0.4kg which is hanging freely. B is moving on the wire with a constant speed of 5m/s. Calculate the magnitude and direction of the reaction of the wire on B.
Resolving for particle of mass 0.4kg:
T = 0.4g.

Let the reaction be R and let it make an angle t with the horizontal.
Resolving horizontally for B gives: 0.4g + Rcost = 0.8(5^2)/(0.4)
Resolving vertically for B gives: Rsint = 0.8g.

Solve the two simultaneous equations to find the value of R and t.

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Updated: February 7, 2005
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