Using the formula for gravity, find the force of gravity on a 0.80-kg mass at Earth's surface. (The mass of Earth is 6×10^24kg, and its radius is 6.4×10^6m.).
F = G * (m₁ m₂) / r²
F = 6.7E-11 * 4.8E24 / (6.4E6)² N
Using the formula for gravity, find the force of gravity on a 0.80-kg mass at Earth's surface. (The mass of Earth is 6×1024kg, and its radius is 6.4×106m.).
Express your answer to two significant figures and include the appropriate units.
To find the force of gravity acting on a mass at Earth's surface, we can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
where F is the force of gravity, G is the gravitational constant (approximately equal to 6.674 × 10^-11 N•m^2/kg^2), m1 is the mass of the first object (Earth), m2 is the mass of the second object (the 0.80 kg mass), and r is the distance between the centers of the two objects (Earth's radius).
Given:
Mass of Earth (m1) = 6 × 10^24 kg
Mass of the object (m2) = 0.80 kg
Radius of Earth (r) = 6.4 × 10^6 m
Gravitational constant (G) = 6.674 × 10^-11 N•m^2/kg^2
Now we can plug in the values into the formula:
F = (6.674 × 10^-11 N•m^2/kg^2 * 6 × 10^24 kg * 0.8 kg) / (6.4 × 10^6 m)^2
First, let's calculate the denominator:
(6.4 × 10^6 m)^2 = (6.4 × 10^6 m) * (6.4 × 10^6 m) = 40.96 × 10^12 m^2
Now, let's substitute this value in the formula:
F = (6.674 × 10^-11 N•m^2/kg^2 * 6 × 10^24 kg * 0.8 kg) / (40.96 × 10^12 m^2)
Next, we can simplify the fraction:
F = (6.674 × 6 × 0.8) / 40.96 × 10^-11 × 10^24 × 10^12
F = (26.9944 × 10^13) / (40.96 × 10^-11) N
Finally, let's calculate the force of gravity:
F ≈ 0.6601 N
Therefore, the force of gravity on the 0.80 kg mass at Earth's surface is approximately 0.6601 Newtons (N).
To find the force of gravity on a 0.80 kg mass at Earth's surface, we can use the formula for the force of gravity:
F = (G * m1 * m2) / r^2
Where:
F is the force of gravity,
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2),
m1 is the mass of one object,
m2 is the mass of the other object,
r is the distance between the centers of the two objects.
In this case, we can assume that the 0.80 kg mass is the object experiencing the gravitational force, and the mass of the Earth is the attracting object. The distance between the center of the two objects is equal to the radius of the Earth.
Substituting the given values into the formula, we have:
F = (6.67430 × 10^-11 m^3 kg^-1 s^-2 * 0.80 kg * 6×10^24 kg) / (6.4×10^6 m)^2
Now let's calculate the force.