1) 29.4 N
The force of gravity between two objects is given by:
where
G is the gravitational constant
M and m are the masses of the two objects
r is the separation between the centres of mass of the two objects
In this problem, we have
(mass of the Earth)
(mass of the box)
(Earth's radius, which is also the distance between the centres of mass of the two objects, since the box is located at Earth's surface)
Substituting into the equation, we find F:
2)
Let's now calculate the ratio F/m. We have:
F = 29.4 N
m = 3.0 kg
Subsituting, we find
This is called acceleration of gravity, and it is the acceleration at which every object falls near the Earth's surface. It is indicated with the symbol .
We can prove that this is the acceleration of the object: in fact, according to Newton's second law,
where a is the acceleration of the object. Re-arranging,
which is exactly equal to the quantity we have calculated above.