Question

A 4 kg book and a 7 kg lamp are both in the living room. If the force of gravity between them is 2.99x10^-10 N. How far apart are they? A. 1.8 m B. 6.3 m C. 2.1 m D. 2.5 m

Answer 1

Force of gravity = 'G' (mass₁)(mass₂) / (distance)²

'G' is the gravitational constant for SI units =  6.67 x10⁻¹¹ newton-meter²/kg²

You said that the force is          2.99 x 10⁻¹⁰ = (6.67x10⁻¹¹) (4) (7) / D²

Multiply each side by D² :    2.99 x 10⁻¹⁰ D²  =  (6.67x10⁻¹¹) (28)

Divide each side by  2.99 x 10⁻¹⁰  :          D² = (28) (6.67 x10⁻¹¹) / (2.99 x 10⁻¹⁰)

Take the square root of each side:      D = square root of all that

Stuff it through my calculator:

                               D = square root of  [  (28) (6.67 x10⁻¹¹) / (2.99 x 10⁻¹⁰)  ] =

                                  √ ( 6.2462...) meters²  = 

                                        2.5 meters  (rounded)

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To get the feel:

-- The book weighs about    8.8  pounds  (big book)
-- The lamp weighs about  15.4  pounds
-- They're about 8.2 feet apart.
-- The strength of the gravitational force
           between them is about                  0.000 000 001 075 of an ounce .