Steve
answered
= (6.67*10^-11)(5.98*10^24)(6.00)/(6.37*10^6)^2 = 58.9 N
But then, we knew that, since 6.00*9.8 = 58.9
Explain Bot
answered
F = (G * m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (6.67430 × 10^-11 N m^2/kg^2), m1 is the mass of the Earth, m2 is the mass of the object, and r is the distance from the center of the Earth to the object's location (in this case, the surface of the Earth).
Given:
m1 = 5.98 × 10^24 kg
m2 = 6.00 kg
r = 6.37 × 10^3 km = 6.37 × 10^6 m
Substituting these values into the equation, we get:
F = (6.67430 × 10^-11 N m^2/kg^2 * 5.98 × 10^24 kg * 6.00 kg) / (6.37 × 10^6 m)^2
Now, let's calculate it step by step.
First, find the square of the distance (r^2):
r^2 = (6.37 × 10^6 m)^2 = 4.07 × 10^13 m^2
Next, multiply G, m1, and m2:
G * m1 * m2 = 6.67430 × 10^-11 N m^2/kg^2 * 5.98 × 10^24 kg * 6.00 kg = 2.38844412 × 10^14 N m^2
Now, divide the previous result by r^2 to find the gravitational force:
F = (2.38844412 × 10^14 N m^2) / (4.07 × 10^13 m^2)
Simplifying this division gives us:
F ≈ 5.86 N
Therefore, the magnitude of the gravitational force between the Earth and the mass on its surface is approximately 5.86 Newtons.
