a A horizontal wire is hung from the ceiling of a room by two massless strings.
ID: 2279066 • Letter: A
Question
a
A horizontal wire is hung from the ceiling of a room by two massless strings. The wire has a length of 0.21 m and a mass of 0.009 kg. A uniform magnetic field of magnitude 0.070 T is directed from the ceiling to the floor. When a current of I = 37 A exists in the wire, the wire swings upward and, at equilibrium, makes an angle ?with respect to the vertical, as the drawing shows. Find (a) the angle and (b) the tension in each of the two strings.
A horizontal wire is hung from the ceiling of a room by two massless strings. The wire has a length of 0.21 m and a mass of 0.009 kg. A uniform magnetic field of magnitude 0.070 T is directed from the ceiling to the floor. When a current of I = 37 A exists in the wire, the wire swings upward and, at equilibrium, makes an angle ?with respect to the vertical, as the drawing shows. Find (a) the angle and (b) the tension in each of the two strings.Explanation / Answer
Draw a free body diagram about the wire. Looking down the wire we have weight (m*g) acting down, The FB (force from the magnetic field) to the rt = I*L*B and the tension T in the strings acting along the strings. (Due to symmetry the tension in each string is the same)
Now sum forces in the vertical we have 2*T*cos(?) = m*g
And in the horizontal I*L*B = 2*T*sin(?)
So dividing the 2nd eqn by the first to eliminate T
we get sin(?)/cos(?) = tan(?) = I*L*B/m*g = 37*0.21*0.070/(0.009*9.8) = 6.17
so ? = arctan(6.17) = 80.8
b) therefore the tension in each string is T = m*g/(2*cos(?)) = 0.009*9.8/(2*cos(80.8)) = 0.276N
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