In this problem, you will calculate the location of the center of mass for the Earth-Moon system. The mass of the Moon is 7.35x10^22 kg, the mass of the Earth is 6.00x10^24 kg, and the mass of the sun is 2.00x10^30 kg. The distance between the Moon and the Earth is 3.80x10^5 km. The distance between the Earth and the Sun is 1.50x10^8 km.
Calculate the location xcm of the center of mass of the Earth-Moon system. Use a coordinate system in which the center of the Earth is at x=0 and the Moon is located in the positive x-direction. Express your answer in kilometers to three significant figures.

The centre of mass of the Earth-moon system is 4600 km from the centre of the Earth.

Centre of mass is at x = +4600 km

Explanation:

Given,

Mass of the moon = (7.35×10²²) kg

Mass of the Earth = (6.00×10²⁴) kg

Mass of the Sun = (2.00×10³⁰) kg

Distance between the Earth and the moon = (3.80×10⁵) km

Distance between the Earth and the Sun = (1.50×10⁸) km

With the right assumption that the Earth and the moon are on the same straight line on the x-axis,

Centre of mass is given as

C.M = (Σmx)/(Σm)

For the Earth-moon system, let the centre of the earth be at x=0, then the moon is at x = (3.80×10⁵) km away on the positive x-axis.

C.M = (Σmx)/(Σm)

Σmx = (6.00×10²⁴) × (0) + (7.35×10²²) × (3.80×10⁵) = (2.793 × 10²⁸) kg.km

Σm = (6.00×10²⁴) + (7.35×10²²) = (6.0735 × 10²⁴) kg

CM = (2.793 × 10²⁸) ÷ (6.0735 × 10²⁴)

CM = (4.599 × 10³) km = 4599 km = 4600 km to 3 s.f

The centre of mass of the Earth-moon system is 4600 km from the centre of the Earth.

Hope this Helps!!!

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.

c. magnitude and direction