Question

A horizontal wire is hung from the ceiling of a room by two massless strings. The...

A horizontal wire is hung from the ceiling of a room by two massless strings. The wire has a length of 0.22 m and a mass of 0.009 kg. A uniform magnetic field of magnitude 0.075 T is directed from the ceiling to the floor. When a current of I = 31 A exists in the wire, the wire swings upward and, at equilibrium, makes an angle φ with respect to the vertical, as the drawing shows. Find (a) the angle and (b) the tension in each of the two strings.

φ =_______ degrees

T= _______ N

Homework Answers

Answer #1

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(φ) = m*g
And in the horizontal I*L*B = 2*T*sin(φ)

So dividing the 2nd eqn by the first to eliminate T

we get sin(φ)/cos(φ) = tan(φ) = I*L*B/m*g = 31*0.22*0.075/(0.009*9.8) = 5.7993

so φ = arctan(5.7993) = 80.216o

b) therefore the tension in each string is T = m*g/(2*cos(φ)) = 0.009*9.8/(2*cos(81.216)) = 0.2887N

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Two blocks are attached by a massless wire block A has a mass of 0.75kg and...
Two blocks are attached by a massless wire block A has a mass of 0.75kg and block B has a mass of 1kg. The blocks have coefficients of static friction µkA =0.5 and µkB=0. The blocks slide down the slope which is at an angle θ =25º to the horizontal. a) Draw a free body diagram of each block indicating the coordinate system and labelling all of the forces on the blocks b) Write down two Newton’s second law equations...
1. For a stationary ball of mass m = 0.200 kg hanging from a massless string,...
1. For a stationary ball of mass m = 0.200 kg hanging from a massless string, draw arrows (click on the “Shapes” tab) showing the forces acting on the ball (lengths can be arbitrary, but get the relative lengths of each force roughly correct). For this case of zero acceleration, use Newton’s 2nd law to find the magnitude of the tension force in the string, in units of Newtons. Since we will be considering motion in the horizontal xy plane,...
1. A rectangular loop of wire with sides 0.142 and 0.528 m lies in a plane...
1. A rectangular loop of wire with sides 0.142 and 0.528 m lies in a plane perpendicular to a constant magnetic field (see part a of the drawing). The magnetic field has a magnitude of 0.604 T and is directed parallel to the normal of the loop's surface. In a time of 0.104 s, one-half of the loop is then folded back onto the other half, as indicated in part b of the drawing. Determine the magnitude of the average...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT