Respuesta :
The solution would be like this for this specific problem:
F = (G Me Mo) / Re^2
F / Mo = (G Me) / Re^2
G = gravitational constant = 6.67384 * 10^-11 m3 kg-1 s-2
Me = 5.972 * 10^24 kg
Re^2 = (6.38 * 10^6)^2 m^2 = 40.7044 * 10^12 m^2 = 4.07044 * 10^13 m^2
G Me / Re^2 = (6.67384 * 10-11 * 5.972 * 10^24) / 4.0704 * 10^13 = 9.7196 m/s^2
9.7196 m/s^2 = acceleration
due to Earth’s gravity
Therefore, the value of the composite constant (Gme / r^2e) that is to be
multiplied by the mass of the object mo in the equation above is 9.7196
m/s^2.
The value of the composite constant is to be multiplied by the mass of object is [tex]\boxed{9.819\text{ m/s}^2}[/tex].
Further explanation:
We have to find the composite constant.
From the Newton’s law of the gravitation, gravitational force exerted by earth on the object at the surface of the earth can be calculated as,
[tex]\boxed{F=\dfrac{{G{M_e}{m_o}}}{{{R_e}^2}}}[/tex]
Here, [tex]G[/tex] is the gravitational constant and its value is [tex]6.674 \times10^{-11}\text{ m}^3/\text{kg}\cdot\text{s}^2[/tex].
[tex]{M_e}[/tex] is the mass of the Earth which is [tex]5.972\times10^{24}\text{ kg}[/tex].
[tex]{m_o}[/tex] is the mass of object on surface of the Earth in kg
[tex]{R_e}[/tex] is the distance between the center of Earth to the center of the object that is the radius of the Earth which is equal to [tex]6.371 \times {10^6}\,{\text{m}}[/tex].
So, the gravitational force exerted by earth on the object of unit mass at the surface of the earth can be calculated as,
[tex]{F_1}=\dfrac{{G{M_e}}}{{{R_e}^2}}[/tex]
Substitute the value of [tex]G[/tex] as [tex]6.674 \times10^{-11}\text{ m}^3/\text{kg}\cdot\text{s}^2[/tex], value of [tex]{M_e}[/tex] as [tex]5.972\times10^{24}\text{ kg}[/tex] and value of [tex]{R_e}[/tex] as [tex]6.371\times{10^6}\text{m}[/tex] in above equation.
[tex]\begin{aligned}{F_1}&=\frac{{\left( {6.674 \times {{10}^{ - 11}}} \right)\left( {5.972 \times {{10}^{24}}} \right)}}{{{{\left( {6.371 \times {{10}^6}} \right)}^2}}}\\&=\frac{{\left( {3.9857 \times {{10}^{14}}} \right)}}{{40.59 \times {{10}^{12}}}}\\&=9.819\text{ m/s}^2\\\end{aligned}[/tex]
This value is equal to the acceleration due to earth’s gravity.
Therefore the value of the composite constant is to be multiply by the mass of the object in the above equation is [tex]\boxed{9.819\text{ m/s}^2}[/tex].
Learn more:
1. A 50 kg meteorite moving at a speed of 1000m/s https://brainly.com/question/6536722
2. The changes experienced by an object under the unbalanced force https://brainly.com/question/2720955
3. A rocket being thrust upward as the force of the fuel https://brainly.com/question/11411375
Answer detail:
Grade: Senior School
Subject: Physics
Chapter: Gravitation
Keywords:
Composite constant, mass, object, Gravitational constant, Mo, Me, G, mass of Earth, object, 6.67X10^-11, 5.972x10^24 kg.
