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3. The thin, uniform rod shown below has negligible mass and and a length of 0.200 m. It is attached to the floor by a frictionless hinge at point P. A horizontal spring with force constant k = 4.80 N/m connects the other end of the rod to a vertical wall. The rod is in a uniform magnetic field of B = 0.340 T directed into the plane of the page. There is a current of /= 6.50 A in the rod, as shown. a. Calculate the torque due to the magnetic force on the rod for an axis at point P. Do this by defining a differential magnetic force on the rod for a differential length dr at an arbitrary distance r from point P. Relate this differential magnetic force to its differential torque at point P. Then sum (i.e., integrate) the contributions from the entire length of the rod to get the total torque on the rod. b. Consider Hooke's Law, which states that the force exerted by the spring when stretched or compressed a length x is Fspring = kx. Now, given that the rod makes an angle of 53.0° with the floor when it is in equilibrium, find the length x and state whether the spring is stretched or compressed. × B X ☑ X P X 53.0° x
Transcribed Image Text:3. The thin, uniform rod shown below has negligible mass and and a length of 0.200 m. It is attached to the floor by a frictionless hinge at point P. A horizontal spring with force constant k = 4.80 N/m connects the other end of the rod to a vertical wall. The rod is in a uniform magnetic field of B = 0.340 T directed into the plane of the page. There is a current of /= 6.50 A in the rod, as shown. a. Calculate the torque due to the magnetic force on the rod for an axis at point P. Do this by defining a differential magnetic force on the rod for a differential length dr at an arbitrary distance r from point P. Relate this differential magnetic force to its differential torque at point P. Then sum (i.e., integrate) the contributions from the entire length of the rod to get the total torque on the rod. b. Consider Hooke's Law, which states that the force exerted by the spring when stretched or compressed a length x is Fspring = kx. Now, given that the rod makes an angle of 53.0° with the floor when it is in equilibrium, find the length x and state whether the spring is stretched or compressed. × B X ☑ X P X 53.0° x
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