Home > Physics > Newton's Law of Gravitation

Two objects have masses of #6# #MG# and #8# #MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #340# #m# to #160# #m#?

Answer 1

At #340# #m# the gravitational potential energy between the masses is #-9.4xx10^-6# #J# and at #160# #m# it is #2.0xx10^-5# #J#.

The change is #-1.91xx10^-5# #J#.

Note that "mg" is a milligram, #10^-3# #g#, but #MG# is a megagram, #10^6# #g#. This is equal to #10^3# #kg#, and since #kg# is the #SI# unit and the gravitational constant is expressed in terms of it, that is the unit we will use.

#U=-(Gm_1m_2)/r# where #G=6.67xx10^-11# #m^3 kg^-1 s^-2#

At #340# #m#:

#U=-(Gm_1m_2)/r=-(6.67xx10^-11xx6xx10^3xx8xx10^3)/340#

#=-(3.2xx10^-3)/340=-9.4xx10^-6##J#

At #160# #m#:

#U=-(Gm_1m_2)/r=-(6.67xx10^-11xx6xx10^3xx8xx10^3)/160#

#=-(3.2xx10^-3)/160=-2.0xx10^-5##J#

The change is (final-initial) #=-2.0xx10^-5-(-9.4xx10^-6)=-1.91xx10^-5# #J#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Nora Arzate

The change in gravitational potential energy between the objects is 6.08 × 10^13 J.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.