Hint: for part I use G = 6.67 times 10 to the
negative 11. for part II, you don’t need to
do the full calculation, you can just use your
knowledge of how force of gravity depends on
mass and separation distance.
Compare the gravitational force on a 49 kg
mass at the surface of the Earth (with ra-
dius 6.4 × 106 m and mass 6 × 1024 kg) with
that on the surface of the Moon �with mass
1
81.3
ME and radius 0.27RE�.
What is the force on the Earth?
Answer in units of N.
Your 1 and 81.3 makes no sense to me.
oh sorry it means 1/81.3
To compare the gravitational force on a 49 kg mass at the surface of the Earth with that on the surface of the Moon, we need to use the formula for gravitational force:
F = (G * m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (6.67 × 10^-11 N m^2 / kg^2), m1 and m2 are the masses of the objects, and r is the separation distance between the centers of the objects.
For the Earth, the mass is given as 6 × 10^24 kg and the radius is given as 6.4 × 10^6 m. Let's calculate the force on the Earth:
F_earth = (G * m1 * m_earth) / r_earth^2
Now, plug in the values:
F_earth = (6.67 × 10^-11 N m^2 / kg^2) * (49 kg) * (6 × 10^24 kg) / (6.4 × 10^6 m)^2
Simplifying the calculation:
F_earth = (6.67 × 10^-11 N m^2 / kg^2) * (49 kg) * (6 × 10^24 kg) / (6.4 × 10^6 m)^2
= (6.67 × 10^-11 N m^2 / kg^2) * (49 * 6 × 10^24 / 6.4^2) kg / m^2
= (6.67 × 10^-11 N m^2 / kg^2) * (49 * 6 × 10^24 / 41) kg / m ^2
= 3.96 × 10^23 N
So, the gravitational force on the Earth is approximately 3.96 × 10^23 N.
Note that the answer is given in units of Newtons (N), which is the unit of force.