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 10 10 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 = √²²² F(x) dx. == Րաշ 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 × 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 × 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) KE27.5×109 J Submit Previous Answers Part E 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+ √²² F(x) dx. When F(x) is constant, F(x) = Fo, and the result of the integral is simply Fo▲x. 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. Evaluate the final kinetic energy of the supply spacecraft for the actual tractor beam force, F(x) = ax³ +ß. ▸ View Available Hint(s) KE2 = ☐ HÅ Value 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 10 10 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 = √²²² F(x) dx. == Րաշ 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 × 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 × 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) KE27.5×109 J Submit Previous Answers Part E 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+ √²² F(x) dx. When F(x) is constant, F(x) = Fo, and the result of the integral is simply Fo▲x. 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. Evaluate the final kinetic energy of the supply spacecraft for the actual tractor beam force, F(x) = ax³ +ß. ▸ View Available Hint(s) KE2 = ☐ HÅ Value Units ?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter6: Energy Of A System

Section: Chapter Questions

Problem 57P

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