2010_exam2_solutions2

# 2010_exam2_solutions2 - Solutions to 10-19 10 a Use Newtons...

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Solutions to 10-19 10. a) Use Newton’s 2 nd law of rotation for the pulley and the ordinary 2 nd law for the falling weight. Set the torque around the pulley = RT = I  and for weight find mg-T=ma. Finally realize that =a/R. Then 2 2 1 () 2 and - sosolvefor /2 6.7m/s 1 2 a RT I MR R mg T ma T TM a mg Ma ma m so a g mM    11. Balance the forces in the y direction: sin /sin 1600 Tm g g N 12. Set the potential energy at height 2R E equal to the sum of potential and kinetic at the earth’s surface: 2 1 0 22 EE GM m GM m PE PE KE mv RR      13. Use =I  or 11 12 2 2 12 2 2 R FR F II mR 14. Use energy conservation, set object’s KE+PE at the planet’s surface to zero, which is total energy of an object at rest at infinity. Get escape velocity 2 GM R where M is the planet’s mass and R it’s radius. So if the new planet has mass 2x that of earth, and half the radius, the factor GM/R increases by 4, so the square root goes up by 2.

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2010_exam2_solutions2 - Solutions to 10-19 10 a Use Newtons...

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