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You are working in a factory that produces long bars of copper with a square cross section. In one section of the production process, the bars must slide down an inclined plane of angle θ. It has been found that the bars travel with too high a speed and become dented or bent when they arrive at the bottom of the plane and must be discarded. In order to prevent this waste, you devise a way to deliver the bars at the bottom of the plane at a lower speed. You replace the inclined plane with a pair of parallel metal rails, shown in Figure P30.19, separated by a distance ℓ. The smooth bars of mass m will slide down the smooth rails, with the length of the bar always perpendicular to the rails. The rails are immersed in a magnetic field of magnitude B, and a resistor of resistance R is connected between the upper ends of the rails. Determine the magnetic field necessary in your device so that the bars will arrive at the bottom of the plane with a maximum speed vmax.
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Chapter 30 Solutions
Physics for Scientists and Engineers
- The potential energy of two atoms in a diatomic molecule can be approximated by the Lennard- Jones potential U(r) = a/r¹² — b/r6, where r is the distance between the two atoms, and a and b are positive constants. a) Find the force F(r) on one of the atoms as a function of r. b) Find the equilibrium distance between the two atoms. Is this equilibrium stable? c) Suppose the distance between the two atoms is equal to the equilibrium distance found in part b). What minimum energy must be added to the molecule to break the two atoms apart? (This is called the dissociation energy of the molecule.)arrow_forwardA smooth circular hoop with a radius of 0.500 m is placed flat on the floor. A 0.400-kg particle slides around the inside edge of the hoop. The particle is given an initial speed of 8.00 m/s. After one revolution, its speed has dropped to 6.00 m/s because of friction with the floor. (a) Find the energy transformed from mechanical to internal in the particle–hoop–floor system as a result of friction in one revolution. (b) What is the total number of revolutions the particle makes before stopping? Assume the friction force remains constant during the entire motion.arrow_forwardA large hydroelectric power plant uses water from a reservoir to turn a generator. The water leaves the generator below the dam, 60 m below the level of the reservoir. The plant uses an 85% efficient generator to supply 1.0 GW of electricity. What mass of water flows through the plant each second?arrow_forward
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