Block on an incline A 1.20 kg block slides down a frictionless incline with a slope angle of 42.0°, starting from a height h = 2.30 m above the bottom of the incline, as shown in Figure 6-25. The incline meets a frictionless horizontal surface, at the end of which is a spring in its equilibrium position (k = 460. N/m) used to stop the block. Find the maximum compression of the spring.
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Marble on a Track The marble in Figure 6-26 starts from rest and slides down a frictionless incline from a height h above the ground, and then goes up the circular track of radius r as shown. Derive an expression for the minimum value of the height,h, so that the marble stays in contact with the circular track at the highest point on the track.
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Sliding on a spherical Surface A polar bear cub sits on top of an igloo (Figure 6-28). The surface of the igloo has a spherical curvature and is smooth enough to have negligible friction. The cub begins to slide down the igloo. Determine the angle at which the cub will leave the surface of the igloo.
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Potential Energy and Force in Three dimensions A particle is in a region in which its potential energy is given by 〖U=(3x〗^2-2xy+zx)where the coefficients 3, 2 and 1 have units J/m2. Find an expression for the force acting on the particle, and determine the magnitude of the force at point A(0.5 m, 21.0 m, 0.5 m).
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Hydroelectric Power
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A net like membranous complex of superposed flat saccules with vesicles detaching from the extremities seen in electronic microscopy. What is the observed structure? What is its biological function?