Part E Evaluate the final kinetic energy of the supply spacecraft for the actual tractor beam force, F(x) = ax³ + ß. ► View Available Hint(s) KE2 = Submit μА Value Units Previous Answers Request Answer ?

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<Physics Primer
Integration of Polynomial Functions
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 =
X2
= 52² F(x) dx.
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 is given by F(x) = ax³ + ß, where a 6.1 × 10-⁹ 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 × 10¹ m away from its beginning position at x = 0.0 m.
=
T
Part D
Evaluate the final kinetic energy of the supply spacecraft if the tractor beam force had been Fo.
► View Available Hint(s)
(
KE2 7.5x10⁹ J
14 of 14
Submit
Previous Answers
Correct
If the Jadarian-Ruby had been properly maintained, GAJMO Nermalloy would be able to successfully complete the delivery mission. The result can be found using
KE2 = KE₁+ √² F(x) dx. When F(x) is constant, F'(x) = Fo, and the result of the integral is simply Fox. That is, the measure of work represented by the integral
Cx2
X 1
is exactly the measure of the rectangle with height Fo and width Ax. For functions of other forms, rectangles only approximate the measure, and the integral allows us to
evaluate the measure in the limit that the rectangles ave infinitesimal width and the measure becomes exact.
Transcribed Image Text:<Physics Primer Integration of Polynomial Functions 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 = X2 = 52² F(x) dx. 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 is given by F(x) = ax³ + ß, where a 6.1 × 10-⁹ 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 × 10¹ m away from its beginning position at x = 0.0 m. = T Part D Evaluate the final kinetic energy of the supply spacecraft if the tractor beam force had been Fo. ► View Available Hint(s) ( KE2 7.5x10⁹ J 14 of 14 Submit Previous Answers Correct If the Jadarian-Ruby had been properly maintained, GAJMO Nermalloy would be able to successfully complete the delivery mission. The result can be found using KE2 = KE₁+ √² F(x) dx. When F(x) is constant, F'(x) = Fo, and the result of the integral is simply Fox. That is, the measure of work represented by the integral Cx2 X 1 is exactly the measure of the rectangle with height Fo and width Ax. For functions of other forms, rectangles only approximate the measure, and the integral allows us to evaluate the measure in the limit that the rectangles ave infinitesimal width and the measure becomes exact.
Part E
Evaluate the final kinetic energy of the supply spacecraft for the actual tractor beam force, F(x) = ax³ + ß.
► View Available Hint(s)
HÅ
KE2 = Value
Submit
Units
Previous Answers Request Answer
?
Transcribed Image Text:Part E Evaluate the final kinetic energy of the supply spacecraft for the actual tractor beam force, F(x) = ax³ + ß. ► View Available Hint(s) HÅ KE2 = Value Submit Units Previous Answers Request Answer ?
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