Two objects have masses of #32 MG# and #35 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #4 m# to #24 m#?

Answer 1

Change in Gravitational Potential Energy=#1.5563\ times 10^(-20)J#

The energy of gravitational potential is given by

#U = - \frac{Gm1m2}{r}#

Given that, #m1 = 32mg = 32\times 10^(-6) kg# # m2 = 35mg = 35\times 10^(-6)kg# Initial distance between the objects = #r = 4m# Final distance between the objects =# r= 24m#

The change in gravitational potential energy will be determined as follows:

When #r= 4m #,

#U1 = - \frac{Gm1m2}{4m}#

when # r = 24m#,

#U2 = - \frac{Gm1m2}{24}#

Change in Gravitational Potential Energy = #U2- U1#

=#(- \frac{Gm1m2}{24} ) - ( - \frac{Gm1m2}{4})#

=#(- \frac{Gm1m2}{24} + \frac{Gm1m2}{4})#

=#Gm1m2(- \frac{1}{24} + \frac{1}{4})#

=#Gm1m2(- \frac{1}{24} + \frac{1}{4}(6/6))#

=#Gm1m2(\frac{-1+6}{24} )#

=#Gm1m2(\frac{5}{24} )#

Substitute the values of #G#,#m1 #and #m2#:

The formula is 6.67 x 10^(-11) x 32 x 10^(-6) kg x 35 x 10^(-6) kg x (5/24).

#= 6.67\times32\times35\times(5/24)\times10^(-11-6-6)#

#=6.67\times (5600/24)\times10^(-23)#

=#1556.333\times 10^(-23) J#

=#1.5563\ times 10^(-20)J#

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Answer 2

Benjamin Asiedu

The change in gravitational potential energy between the objects is 2.14 × 10^15 J.

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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.