The formula to calculate the gravitational force between two objects is F_g=\frac{GM_1M_2}{r^2},F g

=
r
2

GM
1

M
2



, where M_1M
1

and M_2M
2

are the masses of the objects, GG is the gravitational constant and rr is the distance between the objects. Solve for M_1M
1

in terms of F_g, F
g

, G, G, M_2M
2

and r. r.

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?