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 ?
Kinematics
A machine is a device that accepts energy in some available form and utilizes it to do a type of work. Energy, work, or power has to be transferred from one mechanical part to another to run a machine. While the transfer of energy between two machine parts, those two parts experience a relative motion with each other. Studying such relative motions is termed kinematics.
Kinetic Energy and Work-Energy Theorem
In physics, work is the product of the net force in direction of the displacement and the magnitude of this displacement or it can also be defined as the energy transfer of an object when it is moved for a distance due to the forces acting on it in the direction of displacement and perpendicular to the displacement which is called the normal force. Energy is the capacity of any object doing work. The SI unit of work is joule and energy is Joule. This principle follows the second law of Newton's law of motion where the net force causes the acceleration of an object. The force of gravity which is downward force and the normal force acting on an object which is perpendicular to the object are equal in magnitude but opposite to the direction, so while determining the net force, these two components cancel out. The net force is the horizontal component of the force and in our explanation, we consider everything as frictionless surface since friction should also be calculated while called the work-energy component of the object. The two most basics of energy classification are potential energy and kinetic energy. There are various kinds of kinetic energy like chemical, mechanical, thermal, nuclear, electrical, radiant energy, and so on. The work is done when there is a change in energy and it mainly depends on the application of force and movement of the object. Let us say how much work is needed to lift a 5kg ball 5m high. Work is mathematically represented as Force ×Displacement. So it will be 5kg times the gravitational constant on earth and the distance moved by the object. Wnet=Fnet times Displacement.
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06d33441-4a0e-4806-bc89-081e6cfd864c%2Fa75feb04-9066-4a79-a8e9-95724864e53f%2F61yyu4h_processed.png&w=3840&q=75)
![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
?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06d33441-4a0e-4806-bc89-081e6cfd864c%2Fa75feb04-9066-4a79-a8e9-95724864e53f%2Fg74y8c_processed.png&w=3840&q=75)
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