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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 whic 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 network 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(z) dz. The net force exerted by the tractor beam is supposed to be constant, Fo= -3.5 x 105 N, but due to improper maintenance of the Jadarian-Ruby, the actual force exerted by the tractor beam as a function of position z is given by F(z) = az³ +8, where a = 6.1 x 10-9 N/m³ and B = -4.1 x 106 N. Assume the supply spacecraft had an initial kinetic energy of KE₁ =2.7 x 10¹¹ J and that the tractor beam force is applied on the spacecraft over a distance of 7.5 x 10¹ m away from its beginning position at z = 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 7.5x10 J 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+ F(z) dz. When F(z) is constant, F(z) = Fo. and the result of the integral is simply F₁ Az. That is, the measure of work represented by the integral is exactly the measure of the rectangle with height Fo and width Az. 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 have infinitesimal width and the measure becomes exact.

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 whic 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 network 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(z) dz. The net force exerted by the tractor beam is supposed to be constant, Fo= -3.5 x 105 N, but due to improper maintenance of the Jadarian-Ruby, the actual force exerted by the tractor beam as a function of position z is given by F(z) = az³ +8, where a = 6.1 x 10-9 N/m³ and B = -4.1 x 106 N. Assume the supply spacecraft had an initial kinetic energy of KE₁ =2.7 x 10¹¹ J and that the tractor beam force is applied on the spacecraft over a distance of 7.5 x 10¹ m away from its beginning position at z = 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 7.5x10 J 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+ F(z) dz. When F(z) is constant, F(z) = Fo. and the result of the integral is simply F₁ Az. That is, the measure of work represented by the integral is exactly the measure of the rectangle with height Fo and width Az. 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 have infinitesimal width and the measure becomes exact.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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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 = xa HÅ Xb Value b X.10n Units X ?
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) KE₂ = xa HÅ Xb Value b X.10n Units X ?
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 Nm). 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 = S²² F(x) dx. -9 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 B = -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 = 7.5x10⁹ J Submit Previous Answers Correct X2 X1 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+ √2² F(x) dx. When F(x) is constant, F(x) = F₁, and the result of the integral is simply FAx. That is, the measure of work represented by the integral 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 have infinitesimal width and the measure becomes exact.
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 Nm). 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 = S²² F(x) dx. -9 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 B = -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 = 7.5x10⁹ J Submit Previous Answers Correct X2 X1 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+ √2² F(x) dx. When F(x) is constant, F(x) = F₁, and the result of the integral is simply FAx. That is, the measure of work represented by the integral 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 have infinitesimal width and the measure becomes exact.
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