Galactic Alliance Junior Mission Officer (GAJMO) Bundit Nermalloy is predicting the kinetic energy of a supply spacecraft, which is being moved in one dimension in the tractor beam of the ship named the Jadarian-Ruby, to ensure that the supply spacecraft doesn't damage the spaceport to which it is being delivered. GAJMO Nermalloy has been instructed to deliver the supply spacecraft with a kinetic energy less than 1010 J (where 1 J = 1 N·m). GAJMO Nermalloy knows that the change in kinetic energy of an object moving in one dimension is equal to the net work performed on it, where net work is the integral of the component of net force in the direction of motion with respect to the position of the of the object. That is: KE2 – KE₁ = √²² F(x) dx. - x2 x1 The net force exerted by the tractor beam is supposed to be constant, Fo −3.5 × 106 N, but due to improper maintenance of the Jadarian-Ruby, the actual force exerted by the tractor beam as a function of position x is given by F(x) = ax³ + ẞ, where a = 6.1 × 109 N/m³ and ẞ= −4.1 × 106 N. Assume the supply spacecraft had an initial kinetic energy of KE₁ = 2.7 × 10¹¹ J and that the tractor beam force is applied on the spacecraft over a distance of 7.5 × 104 m away from its beginning position at x = 0.0 m. Part D Evaluate the final kinetic energy of the supply spacecraft if the tractor beam force had been Fo. ▸ View Available Hint(s) KE2 = ☐ Value о Α Units ?
Galactic Alliance Junior Mission Officer (GAJMO) Bundit Nermalloy is predicting the kinetic energy of a supply spacecraft, which is being moved in one dimension in the tractor beam of the ship named the Jadarian-Ruby, to ensure that the supply spacecraft doesn't damage the spaceport to which it is being delivered. GAJMO Nermalloy has been instructed to deliver the supply spacecraft with a kinetic energy less than 1010 J (where 1 J = 1 N·m). GAJMO Nermalloy knows that the change in kinetic energy of an object moving in one dimension is equal to the net work performed on it, where net work is the integral of the component of net force in the direction of motion with respect to the position of the of the object. That is: KE2 – KE₁ = √²² F(x) dx. - x2 x1 The net force exerted by the tractor beam is supposed to be constant, Fo −3.5 × 106 N, but due to improper maintenance of the Jadarian-Ruby, the actual force exerted by the tractor beam as a function of position x is given by F(x) = ax³ + ẞ, where a = 6.1 × 109 N/m³ and ẞ= −4.1 × 106 N. Assume the supply spacecraft had an initial kinetic energy of KE₁ = 2.7 × 10¹¹ J and that the tractor beam force is applied on the spacecraft over a distance of 7.5 × 104 m away from its beginning position at x = 0.0 m. Part D Evaluate the final kinetic energy of the supply spacecraft if the tractor beam force had been Fo. ▸ View Available Hint(s) KE2 = ☐ Value о Α Units ?
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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Transcribed Image Text:Galactic Alliance Junior Mission Officer (GAJMO) Bundit Nermalloy is predicting the kinetic energy of a supply spacecraft, which is being moved in one dimension in the tractor beam of the ship named the Jadarian-Ruby, to ensure that the supply spacecraft doesn't damage the spaceport to which
it is being delivered. GAJMO Nermalloy has been instructed to deliver the supply spacecraft with a kinetic energy less than 1010 J (where 1 J = 1 N·m). GAJMO Nermalloy knows that the change in kinetic energy of an object moving in one dimension is equal to the net work performed on it,
where net work is the integral of the component of net force in the direction of motion with respect to the position of the of the object. That is: KE2 – KE₁ = √²² F(x) dx.
-
x2
x1
The net force exerted by the tractor beam is supposed to be constant, Fo −3.5 × 106 N, but due to improper maintenance of the Jadarian-Ruby, the actual force exerted by the tractor beam as a function of position x is given by F(x) = ax³ + ẞ, where a = 6.1 × 109 N/m³ and
ẞ= −4.1 × 106 N. Assume the supply spacecraft had an initial kinetic energy of KE₁ = 2.7 × 10¹¹ J and that the tractor beam force is applied on the spacecraft over a distance of 7.5 × 104 m away from its beginning position at x = 0.0 m.
Part D
Evaluate the final kinetic energy of the supply spacecraft if the tractor beam force had been Fo.
▸ View Available Hint(s)
KE2 =
☐
Value
о
Α
Units
?
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