A thin, uniform rod with negligible mass and length 0.200

Chapter 27, Problem 79P

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CP CALC A thin, uniform rod with negligible mass and length 0.200 m is attached to the floor by a frictionless hinge at point P (Fig. P27.79). A horizontal spring with force constant \(k=4.80 \mathrm{~N} / \mathrm{m}\) connects the other end of the rod to a vertical wall. The rod is in a uniform magnetic field \(B=0.340 \mathrm{~T}\) directed into the plane of the figure. There is current \(I=6.50 \mathrm{~A}\) in the rod, in the direction shown. (a) Calculate the torque due to the magnetic force on the rod, for an axis at P. Is it correct to take the total magnetic force to act at the center of gravity of the rod when calculating the torque? Explain. (b) When the rod is in equilibrium and makes an angle of \(53.0^{\circ}\) with the floor, is the spring stretched or compressed? (c) How much energy is stored in the spring when the rod is in equilibrium?

Equation Transcription:

Text Transcription:

k=4.80 N/m

B=0.340 T

I=6.50 A

53.0deg

Vector B

53.0deg