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An object with mass 7 kgmoves from a location <22,43,-41> near the Earth's surface to location<-27,11,46>m. What is the change in the potential energy of the system consisting of the object plus the Earth?

Short Answer

Expert verified

The change in potential energy of the system is -2200J.

Step by step solution

01

Identification of the given data

The given data is listed as follows,

  • The mass of the object is,m=7 kg
  • The initial location is, r,=22,43,-41m
  • The final location is, r,=-27,11,46m
02

Expression of change in potential energy and gravitational force

The change in potential energy is expressed as,

U=F鈬赌(r鈬赌f-r鈬赌i)

Here,r鈬赌iis the final position,r鈬赌f is the initial position andF鈬赌is force.

The gravitational force acting on the object is shown as,

F=mg

Here, m is the mass, g is the acceleration due to gravity with value 9.8m/s2.

03

Determination of the value of the potential energy of the system

The expression for the change in potential energy is expressed as follows,

U=mgr鈬赌f-r鈬赌i

It is known that the change of potential energy is in thedirection only.

Substitute all the values in the above expression.

U=7kg9.8m/s211m-43m=7kg9.8m/s232m=-2195.2kg-m2/s21J1kgm2/s2=-2195.2J-2200J

Thus, the change in potential energy of the system -2200J.

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http://www.jpl.nasa.gov/sl9/ sl9.html

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