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## Chapter 5 Problems

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**Chapter 5 Problems**• Gravitation: 25,26,29,30,37,38 • Satellites/Apparent Weight: 39,40,41,43,44,49**Chapter 5 Problem 25**• Given • rearth surface to spaceship =12800km=1.28x107m • rearth center to spaceship =1.28x107m+6.38106m • m=1400kg • Find • Fg =? N • FRSA • Fg= G mme = 6.67x10-11 Nm2/kg2(1400kg)(5.98x1024kg) • r2 (1.28x107m+6.38106m)2 • Fg=1520 N**Chapter 5 Problem 29**• Given: • m=2.10kg • g = 12.0 m/s/s • Find • m=? Kg • Weight = Fg=?N • FRSA • m = 2.10 kg • Weight = Fg = mg = 2.10kg( 12.0 m/s/s) = 25.20 N**Chapter 5 Problem 26**• Given Find • mmoon = 7.35x1022kggmoon = ? m/s/s • mearth = 5.98 x1024 kg • rmoon = 1.74x106m mgmoon = G mmm • rearth = 6.38 x106 m r2moon • g = 9.8 m/s/s mgearth = G mmm • r2earth • gmoon = gearthmmoon (r2earth) • mearth (r2moon) • gmoon = (9.8m/s/s)(7.35x1022kg)(6.38 x106 m)2 =1.62m/s/s • (5.98 x1024 kg)(1.74x106m)2**Chapter 5 Problem 30**• Given • rearth surface to 300km =300km=3.00x107m • rearth center to 300km =3.00x105m+6.38106m • m=80kg • Find • Fg =? N • FRSA • Fg= G mme = 6.67x10-11 Nm2/kg2(80kg)(5.98x1024kg)=715 N • r2 (3.00x105m+6.38106m)2 91% • Fg= G mme = 6.67x10-11 Nm2/kg2(80kg)(5.98x1024kg)=784 N • r2 (6.38106m)2**Chapter 5 Problem 37**• Given Fin • mmars =? • mearth = 5.98 x1024 kg • rmoon = 3.20x106m mgmars = G mmm • rearth = 6.38 x106 m r2mars • gearth = 9.8 m/s/s mgearth = G mmm • gmars =.32(9.8m/s/s)r2earth • =3.14m/s/s gmars (r2mars ) mearth = mmoon • gearth (r2earth) • mmars = (314m/s/s)(3.2 x106 m)2 (5.98 x1024 kg)=4.72x1024kg • (6.38x106m)2**Chapter 5 Problem 38**• Given • t=1year (365d)(24hr)(60min)(60sec)=3.15x107s • (1year)(1day)(1hr )(1min ) • r=1.51x1011m • Find • msun • FRSA • Fg=Fc • Gmms= mv2 ms = rv2= • r2 r G msun(1.51x1011m)(2p(1.51x1011m)/3.15x107s)2 6.67x10-11 Nm2 / kg2 msun=2.0x1030kg**Chapter 5 Problem 39**• Given3600km • r=6.38x106m+3.6x106 m =9.98x106m • Find • msun • FRSA • Fg=Fc • Gmms= mv2 Gme = v = 6.67x10-11 (5.98x1024kg) • r2 r r (9.98x106m) • v= 6300 m/s**Chapter 5 Problem 40**• Given • Mmonkey = 17.0kg • FT=220 N • Find • a = ? m/s/s • Fnet = ma • FT – Fg = ma • FT – mg = a = 220N – 17kg(9.8m/s2) = 3.14m/s/s up • m 17kg**Chapter 5 Question 41.**• Given • g = ½ g ½ g = v2 • r = 16m r • Find • v=m/s ½ rg = v = ½ (16m) (9.8m/s/s) = 8.85m/s • FRSA • FN=Fc v = 2 p r • FN=mv2 t • r • m ½ g=mv2 t = 2 p r2 p (16m) = 11 seconds per rev • r v 8.85m/s**Chapter 5 Problem 43**• Given100km • r=1.74x106m+1.0x105 m =1.84x106m mmoon=7.35x1022kg • Find • msun • FRSA • Fg=Fc • Gmmm= mv2 Gmm = v = 6.67x10-11 (7.35x1022kg) • r2 r r (1.84x106m) • v= 1632 m/s v=2pr t = 2pr = 2 p (1.84x106m) = 7083s • t v 1632m/s or (2hrs)**Chapter 5 Problem 44**• S Fy = 0 for at rest, constant up, constant down • FN=Fg FN = mg = 58kg(9.8m/s/s) = 568 N • S Fy = ma for accelerating up • FT-Fg = ma FT-mg= ma FT = mg + ma • FT = (58kg*9.8m/s/s) + (58kg*.33*9.8m/s/s)=756N • S Fy = ma for accelerating down • Fg-FT = ma mg-FT = ma mg – ma=FT • (58kg*9.8m/s/s) - (58kg*.33*9.8m/s/s)=381N • S Fy = ma for free fall • Fg = ma mg=ma g=a and FT=0**Bipolar Star System**Two stars 3.6x1011m apart rotate about a point 1.8x1011 m from each other in a circular path in 5.0 years. The two stars have the same mass. What is the velocity of the stars? What is the mass of the stars?**Bipolar Star System**Two stars 3.6x1011m apart rotate about a point 1.8x1011 m from each other in a circular path in 5.0 years. The two stars have the same mass. What is the velocity of the stars? What is the mass of the stars? 3.6x108m**Bipolar Star System**Two stars 3.6x1011m apart rotate about a point 1.8x1011 m from each other in a circular path in 5.0 years. The two stars have the same mass. . What is the velocity of the stars? What is the mass of the stars? 1.8x1011m**Bipolar Star System**Two stars 3.6x1011m apart rotate about a point 1.8x1011 m from each other in a circular path in 5.0 years. The two stars have the same mass. What is the velocity of the stars? v = 2 p r t**Bipolar Star System**Two stars 3.6x1011m apart rotate about a point 1.8x1011 m from each other in a circular path in 5.0 years. The two stars have the same mass. What is the velocity of the stars? v = 2 p r t v = 2 p ( 1.8x10 11m) = 7170 m/s (5.0yrs(365d)(86400s) ( 1yr )( 1 day )**Bipolar Star System**Two stars 3.6x1011m apart rotate about a point 1.8x1011 m from each other in a circular path in 5.0 years. The two stars have the same mass. What is the mass of the stars? Fg Fg**Bipolar Star System**Two stars 3.6x1011m apart rotate about a point 1.8x1011 m from each other in a circular path in 5.0 years. The two stars have the same mass. What is the mass of the stars? Fg Fg Fg causes the centripetal acceleration therefore Fg = Fc**Bipolar Star System**Two stars 3.6x1011m apart rotate about a point 1.8x1011 m from each other in a circular path in 5.0 years. The two stars have the same mass. What is the mass of the stars? Fg=Fc Fg causes the centripetal acceleration therefore Fg = Fc**Bipolar Star System**Two stars 3.6x1011m apart rotate about a point 1.8x1011 m from each other in a circular path in 5.0 years. The two stars have the same mass. What is the mass of the stars? Fg=Fc G mm = m v2 (8x1010m)2 4x1010m Fg causes the centripetal acceleration therefore Fg = Fc Distance between Distance to centers the center of rotation**Bipolar Star System**Two stars 3.6x1011m apart rotate about a point 1.8x1011 m from each other in a circular path in 5.0 years. The two stars have the same mass. What is the mass of the stars? Fg=Fc G mm = m v2 (3.6x1011m)2 1.8x1011m Fg causes the centripetal acceleration therefore Fg = Fc Distance between Distance to centers the center of rotation**Bipolar Star System**Two stars 3.6x1011m apart rotate about a point 1.8x1011 m from each other in a circular path in 5.0 years. The two stars have the same mass. Fg=Fc G mm = m (7170m/s)2 (3.6x1011m)2 1.8x1011m Fg causes the centripetal acceleration therefore Fg = Fc**Bipolar Star System**Two stars 3.6x1011m apart rotate about a point 1.8x1011 m from each other in a circular path in 5.0 years. The two stars have the same mass. What is the mass of the stars? Fg=Fc G m = (7170m/s)2 (3.6x1011m)2 1.8x1011m Fg causes the centripetal acceleration therefore Fg = Fc**Bipolar Star System**Two stars 3.6x1011m apart rotate about a point 1.8x1011 m from each other in a circular path in 5.0 years. The two stars have the same mass. Fg=Fc G m = (7170m/s)2 (3.6x1011m)2 1.8x1011m m = (7170m/s)2 (3.6x1011m)2 = 5.5x1029 kg 6.67x10-11Nm2/kg2 (1.8x1011m) Fg causes the centripetal acceleration therefore Fg = Fc