Soluciones Fisica Serway

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Algunos ejercicios resueltos de física
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Solutions to Final Exam for GP I, SNME, Fall 2011. 1. 10 % A small block with mass 0.250 kg is attached to a string passing through a hole in a frictionless, horizontal surface (see figure). The block is originally revolving in a circle with a radius of 0.800 m about the hole with a tangential speed of 4.00 m/s. The string is then pulled slowly from below, shortening the radius of the circle in which the block revolves. The breaking strength of the string is 30.0 N. What is the radius of the circle when the string breaks ? Solution Tension T of the string is radial so that it gives no torque on the block. Angular momemtum is therefore conserved, i.e., . Hence ( EMBED Equation.DSMT4 2. 10 % You are trying to raise a bicycle wheel of mass m and radius R up over a curb of height h. To do this, you apply a horizontal force F at the center of the wheel (see figure). What is the smallest magnitude of the force F that will succeed in raising the wheel over the curb ? Solution Perpendicular distance of F to the corner of the curb is R – h. Perpendicular distance of mg to the corner of the curb is . Torques about the corner of the curb: Setting ( ( 0 gives the minimum force required to lift the wheel: 3. 20 % You measure the period of a physical pendulum about one pivot point to be T. Then you find another pivot point on the opposite side of the center of mass that gives the same period. The two points are separated by a distance L. Show that . Solution For a physical pendulum . Let the distances of the pivot points to the CM be d1 and d2 . We have ( From the parallel axis theorem, we have · 4. 20% A cylindrical container of an incompressible liquid of density ( rotates with constant angular speed ( about its axis of symmetry, which we take to be the y axis (see figure). Find the height h of the liquid surface as a function of r. Solution Pressure p is a function of both y and r. Let the liquid surface at be the origin of the y –axis. Then for the pressure on the plane , ( Using with where pA is the atmospheric pressure, we have or 5. 20% A 5.00 m, 0.732 kg wire is used to support two uniform 235 N posts of equal length (see figure). A strong wind is blowing, causing the wire to vibrate in its 7th overtone (8th harmonic). Assume the wire is essentially horizontal and that the speed of sound in air is 344 m/s. What are the frequency and wavelength of the sound this wire produces? Hint: The frequency of the sound wave (in air) is equal to the frequency of the standing wave in the vibrating wire. Solution Torques about left pivot point: EMBED Equation.DSMT4 Velocity of wave on wire is given by . Hence, For the 8th harmonic, wavelength of standing wave is Its frequency is The frequency of the sound wave is therfore 18.3 Hz. Its wavelength is 6. 10% + 10% A spherical shell has inner and outer radii a and b, respectively, and the temperatures at the inner and outer surfaces are T1 and T2. The thermal conductivity of the material of which the shell is made is k. (a) Find the total heat current through the shell. (b) Find T within the shell as a function of r, the distance from the center of the shell. Hint: for all , and . Solution (a) ( EMBED Equation.DSMT4 EMBED Equation.DSMT4 (b) EMBED Equation.DSMT4 EMBED Equation.DSMT4 _1387113112.unknown _1387358659.unknown _1387359825.unknown _1387360997.unknown _1387361092.unknown _1387360988.unknown _1387358908.unknown _1387359574.unknown _1387359780.unknown _1387359040.unknown _1387358724.unknown _1387270986.unknown _1387271641.unknown _1387271731.unknown _1387271841.unknown _1387272093.unknown _1387358599.unknown _1387271995.unknown _1387271798.unknown _1387271660.unknown _1387271298.unknown _1387271317.unknown _1387271463.unknown _1387271012.unknown _1387113283.unknown _1387270885.unknown _1387113201.unknown _1387113248.unknown _1387095884.unknown _1387096813.unknown _1387113015.unknown _1387113029.unknown _1387112911.unknown _1387112944.unknown _1387112823.unknown _1387096529.unknown _1387096591.unknown _1387096682.unknown _1387096130.unknown _1387096482.unknown _1387096095.unknown _1387093843.unknown _1387094077.unknown _1387095763.unknown _1387093927.unknown _1387093627.unknown _1387093765.unknown _1387093559.unknown
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