Done AA valenciacollege.quiz-Iti-iad-prod.instructure.com C Return Submit -71 5.8 Use the work-energy theorem to determine an expression Escape Velocity for the initial velocity, vo of the projectile at RE so that the "In celestial mechanics Ex, escape velocity or escape speed is the final velocity as R-> co is vf = 0. (This is called Earth's escape minimum speed needed for a free, non-propelled E object to escape velocity) from the gravitational influence of a primary body Ex, thus reaching an infinite distance from it." -- Wikipedia/Escape velocity. E O 29ME 1 VO = RE This set of questions will lead you to calculate the escape velocity (from Earth and from Newtonian Black Holes!.) Try RE E them yourself first, but if you need hints, you can follow along 2GME with this video explanation Ex. 2GME 2 VO = RE Recall: O RE vo 7 . The work done in moving an object from a to b by a 2GME force which varies with position F = F (r ) is given by: 13 1 point W = SF . dT If the Earth's radius is RE~6300 km and has a mass of approximately 5.9 x 1024 kg, estimate Earth's escape 8 velocity. . The force of Earth's gravity on a projectile of mass m launched from Earth's surface is given by: O vo = 1.12 . 104 m F ( T ) = -- vo = 1.25 . 108 m E 7 2 GMEm +, where G ~ 6.67 . 10-11 Nm2 kg2 vo = 3.52 . 1010 m S 10 O Vo = 4.28 . 109 mDone AA valenciacollege.quiz-Iti-iad-prod.instructure.com C Return Submit from the gravitational influence of a primary body Ex, thus reaching 13 Tpoint X an infinite distance from it." -- Wikipedia/Escape velocity E If the Earth's radius is RE~6300 km and has a mass of This set of questions will lead you to calculate the escape approximately 5.9 x 1024 kg, estimate Earth's escape velocity. velocity (from Earth and from Newtonian Black Holes!.) Try them yourself first, but if you need hints, you can follow along O vo = 1.12 . 10*m with this video explanation Ex. vo = 1.25 . 108 m E Recall: O vo = 3.52 . 1010 m . The work done in moving an object from a to b by a 1 force which varies with position F = F (r) is given O vo = 4.28 . 109 by : E W = SF . dT 14 1 point A black hole of mass Moh = 6.00 x 1030 kg (about 3 solar . The force of Earth's gravity on a projectile of mass m masses) has an escape velocity of c = 3 x 108 m/s (the speed launched from Earth's surface is given by: of light) at a spherical surface called the event horizon. Determine the radius of the event horizon. This is called the GMEm , where G ~ 6.67 . 10-11 Nm2 black hole's Schwarzschild radius. F ( T ) =-- kg2 E O Vescape = 2.67 . 10 2m O Vescape = 1.31 . 1015 m 8 O Vescape = 8.89 . 103 m O Vescape = 1.80 . 1037 m E Submit 10Done AA valenciacollege.quiz-Iti-iad-prod.instructure.com C Return Submit Pete on the roof again 8 1 point Pete is patching his roof -- he places his 5.0 kg toolbox on the roof, which is inclined at 25 degrees with the horizontal. The Calculate the net work done on the box as it slides the length coefficient of kinetic friction between the box and the roof is of the roof (6.0m) 0.15 84.3 E 1 9 1 point Use the work-energy theorem to find the speed of the E toolbox when it reaches the edge of the roof. 5.8 Escape Velocity 10 1 point "In celestial mechanics Ex, escape velocity or escape speed is the minimum speed needed for a free, non-propelled E object to escape Determine an expression for the work done by gravity on the from the gravitational influence of a primary body Ex, thus reaching Earth-projectile system in launching the projectile from an infinite distance from it." -- Wikipedia/Escape velocity Earth's surface at RE vertically to a distance R where R > RE. 8 Your expression should be in terms of G, m, ME, RE, and R. This set of questions will lead you to calculate the escape GMEm GMEm velocity (from Earth and from Newtonian Black Holes!.) Try O W = RE R them yourself first, but if you need hints, you can follow along O W = GMEm + GMEm with this video explanation Ex R RE E Recall: O W = GMEm GMEm R RRE 10 . The work done in moving an object from a to b by a O W = GMEm GMEmDone AA valenciacollege.quiz-Iti-iad-prod.instructure.com C Return Submit 5.8 -71 Determine an expression for the work done by gravity on the Escape Velocity Earth-projectile system in launching the projectile from Earth's surface at RE vertically to a distance R where R > RE. "In celestial mechanics Ex, escape velocity or escape speed is the Your expression should be in terms of G, m, ME, RE, and R. minimum speed needed for a free, non-propelled E object to escape from the gravitational influence of a primary body Ex, thus reaching O W = GMEm GMEm RE R an infinite distance from it." -- Wikipedia/Escape velocity. E 1 O W = GMEm GMEm This set of questions will lead you to calculate the escape R RE velocity (from Earth and from Newtonian Black Holes!.) Try O E W = GMEm GMEm them yourself first, but if you need hints, you can follow along R RRE with this video explanation Ex. O W = GMEm GMEm 2 R RE Recall: 7 . The work done in moving an object from a to b by a 11 1 point force which varies with position F = F (r ) is given by: Take the limit that R -> to determine an expression for the work needed to launch the projectile to an infinite distance W = SF . dT from Earth. Your expression should be in terms of G, m, ME, RE, and R. 8 . The force of Earth's gravity on a projectile of mass m O W = GREM launched from Earth's surface is given by: ME O W = GMEm GMEm +, where G ~ 6.67 . 10-11 Nm2 RE E F ( T ) = -- 7 2 kg2 O W = RE GMEm 10 O W = GMEm RE