Two objects have masses of #5 MG# and #8 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #140 m# to #160 m#?

Question

Two objects have masses of #5 MG# and #8   MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #140 m# to #160 m#?

Layla Ahmed · Accepted Answer

Change in Gravitational potential energy is #3.4541\times 10^(-24) J#

The energy of gravitational potential is given by

#U=−(Gm1m2)/r#

Given that, #m1=5mg=5×10^-6 # kg

#m2=8mg=8×10^-6 # kg

Initial distance between the objects = #r1=140m#

Final distance between the objects =# r2= 160 m #

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

When #r1= 140m #m

#U1 = −(Gm1m2)/(r1)#

Additionally

When #r2 = 160m#'

#U2 =−(Gm1m2)/(r2)#

Change in Gravitational Potential Energy = #U2 -U1#

=# (−(Gm1m2)/(r2) )- (−(Gm1m2)/(r1))#

=# (−(Gm1m2)/(160) )- (−(Gm1m2)/(140))#

=# (−(7Gm1m2)/(1120) +(8Gm1m2)/(1120))#

=#(Gm1m2)/(1120)#

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

# U2- U1 = (6.67\times 10^(-11) \times 5×10^-6 \times 8×10^-6)/1120 #

# U2- U1 = (386.86\times 10^(-11) \times10^-6 \times 10^-6)/1120 J#

# U2- U1 = (0.34541\times 10^(-11) \times 10^-6 \times 10^-6) J#

# U2- U1 = (0.34541\times 10^(-23) J#

# U2- U1 = 3.4541\times 10^(-24) J#

So, Change in Gravitational potential energy is #3.4541\times 10^(-24) J#

Charlotte Aaron · Answer

undefined The change in gravitational potential energy is 9.8 × 10^12 joules.