Answer:
E11. 0.6 N
E12. 1.61×10⁻⁴ N
E13. 1.12 N
E14. 45 lb
Explanation:
The force due to gravity between two objects is:
F = Gm₁m₂ / r²
where G is the gravitational constant,
m₁ and m₂ are the masses of the objects,
and r is the distance between them.
E11. At a distance r, the force is 9.6 N.
9.6 = Gm₁m₂ / r²
At quadruple the distance (4r), the force is:
F = Gm₁m₂ / (4r)²
F = Gm₁m₂ / (16r²)
F = 9.6 / 16
F = 0.6
E12. Given m₁ = m₂ = 700 kg, and r = 0.45 m:
F = Gm₁m₂ / r²
F = (6.67×10⁻¹¹ m³/kg/s²) (700 kg) (700 kg) / (0.45 m)²
F = 1.61×10⁻⁴ N
E13. At a distance r, the force is 0.28 N.
0.28 = Gm₁m₂ / r²
At half the distance (r/2), the force is:
F = Gm₁m₂ / (r/2)²
F = 4 Gm₁m₂ / r²
F = 4 (0.28)
F = 1.12
E14. The acceleration due to gravity on the Moon is 1/6 that of Earth's. So an astronaut weighs 1/6 as much on the Moon.
W = 270 lb / 6
W = 45 lb
