Calculate the force of gravity on a 10 kg mass if it were 6.4x10^6 m above Earth's surface (that is, if it were 2 Earth radii from Earth's center.)

Twice as far from center of earth so 1/4 of the gravitational force

(1/4)(9.81)(10)

To calculate the force of gravity on an object, we can use the formula:

F = (G * m1 * m2) / r^2

where:
F is the force of gravity,
G is the gravitational constant (approximately 6.67 × 10^-11 N(m/kg)^2),
m1 and m2 are the masses of the two objects (in this case, one of the masses is Earth),
and r is the distance between the centers of the two objects.

In this case, the mass of the object (m1) is given as 10 kg, and the distance between the object and Earth's center (r) is given as 2 Earth radii or 6.4 × 10^6 m.

To calculate the force of gravity, we need to know the mass of Earth (m2). The mass of Earth is approximately 5.97 × 10^24 kg.

Now we can plug in the values into the formula:

F = (6.67 × 10^-11 N(m/kg)^2 * 10 kg * 5.97 × 10^24 kg) / (6.4 × 10^6 m)^2

Simplifying the equation:

F = (6.67 × 10^-11 N(m/kg)^2 * 10 kg * 5.97 × 10^24 kg) / (6.4 × 10^6 m)^2
= (6.67 × 10^-11 N(m/kg)^2 * 10 kg * 5.97 × 10^24 kg) / (4.096 × 10^13 m^2)
= (4.01 × 10^14 N(m/kg)^2 * kg^2) / (4.096 × 10^13 m^2)
= 9.8 N

Therefore, the force of gravity on a 10 kg mass, 6.4 × 10^6 m above Earth's surface, is approximately 9.8 Newtons.