PHYS_2014_Sample_Exam_2_soln-1

PHYS_2014_Sample_Exam_2_soln-1 - PHYS2014 Benton Fall 2010...

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PHYS2014 Fall 2010 Benton OSU Physics Dept. Physics 2014: General Physics I Solutions to Sample Exam No. 2 1. A 0.5 m long spring, having a spring constant of 380 N/m, is suspended from the ceiling by a hook. It can be stretched by an amount Δ s = 0.8 m before it will break. a) What is the maximum mass, M , that can be suspended from the spring without breaking it? b) If we hang a mass of M = 17 kg from the spring, what is the elastic potential energy stored in the spring. Solution: a) Equate Hooke’s Law with the force due to gravity. 2 380N m 0.8m 31kg m 9.80 s F k s mg k s m g = − Δ = − Δ = = = b) First find Δ s resulting from suspension of a 17 kg mass from the spring. Then plug that value into the equation for elastic potential energy. ( ) 2 2 2 m 17kg 9.80 s 0.43m 380N m 1 1 380N m 0.43m 35J 2 2 s F k s mg mg s k U k s = − Δ = − Δ = = = = Δ = = M 0.5 m
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PHYS2014 Fall 2010 Benton OSU Physics Dept. 2. Global Positioning System (GPS) satellites are in circular orbits with orbital periods of exactly 12 hours. a) What is the difference between the radius of the GPS orbit (orbital period of 12 hours) and the radius of a geosynchronous orbit (orbital period of 24 hours)? b) How much work would it take to move a GPS satellite from its standard 12 hour period orbit into a geosynchronous orbit? The mass of a GPS satellite is 1080 kg. Solution: a) We can calculate the radius of an orbit based on its period. Since 2 T π ω = , we can substitute that into the equation for centripetal force and set that equal to Newton’s Law of Gravitation: E M m G 2 m r = 2 2 3 2 2 2 3 2 4 4 E E E r GM GM T r GM T r = = = For the GPS satellite in its original orbit, the period is T GPS = 12 hrs = 43,200 s. For the satellite in geosynchronous (GEO) orbit, the period is T GEO = 24 hrs = 86,400 s. The radii of the two
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PHYS_2014_Sample_Exam_2_soln-1 - PHYS2014 Benton Fall 2010...

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