By compressing the spring a distance <em>x</em> (in m), you are storing 1/2 <em>k</em> <em>x</em> ² (in J) of potential energy, which is converted completely into kinetic energy 1/2 <em>m v</em> ², where
• <em>k</em> = 40 N/m = spring constant
• <em>m</em> = 10 kg = mass of the ball
• <em>v</em> = 2 m/s = ball's speed (at the moment the spring returns to its equilibrium point)
So we have
1/2 <em>k</em> <em>x</em> ² = 1/2 <em>m</em> <em>v</em> ²
<em>x</em> = √(<em>m</em>/<em>k</em> <em>v</em> ²) = √((10 kg) / (40 N/m) (2 m/s)²) = 1 m
m₁ = mass of the first object = 3.0 kg
m₂ = mass of the second object = 3.0 kg
r = distance between the first and second object = 1.0 m
G = universal gravitational constant = 6.67 x 10⁻¹¹ N m²/kg²
F = force of gravity between the two objects = ?
according to law of gravitation, force of attraction "F" between two objects m₁ and m₂, placed distance "r" apart is given as
F = G m₁ m₂/r²
inserting the values
F = (6.67 x 10⁻¹¹) (3.0) (3.0)/(1.0)²
F = (6.67 x 10⁻¹¹) (9.0)
F = 60.03 x 10⁻¹¹ N
F = 6.003 x 10⁻¹⁰ N
