Two objects have masses of #42 MG# and #26 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #8 m# to #9 m#?

Question

Two objects have masses of #42   MG# and #26    MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #8   m# to #9  m#?

Nora Arzate · Accepted Answer

We will use the formula #U=-G(Mm)/r#

We will first calculate the potential energy at 8m

#U_1=-(6.67*10^(-11)*42*26*10^6)/8=-0.009 #Joules

#U_2=-(6.67*10^(-11)*42*26*10^6)/9=-0.008 #Joules

so #ΔU=U_2-U_1=0.001#Joules

the change is positive because the distance gets bigger

(I assumed MG is megagrams.)

Nicholas Agrusa · Answer

undefined To calculate the change in gravitational potential energy (ΔU), you can use the formula:

ΔU = G * ((m1 * m2) / r1) - G * ((m1 * m2) / r2)

Where:
- G is the gravitational constant (approximately 6.674 × 10^-11 N m^2 / kg^2)
- m1 and m2 are the masses of the objects (in kilograms)
- r1 and r2 are the initial and final distances between the objects (in meters)

Given:
- m1 = 42 MG = 42 * 10^6 kg
- m2 = 26 MG = 26 * 10^6 kg
- r1 = 8 m
- r2 = 9 m

Substituting the values into the formula:

ΔU = (6.674 × 10^-11) * ((42 * 10^6) * (26 * 10^6) / 8) - (6.674 × 10^-11) * ((42 * 10^6) * (26 * 10^6) / 9)

Solve for ΔU.