contestada

Which of the following changes to the earth-sun system would reduce the magnitude of the force between them to one-fourth the value found in Part A?

Reduce the mass of the earth to one-fourth its normal value.
Reduce the mass of the sun to one-fourth its normal value.
Reduce the mass of the earth to one-half its normal value and the mass of the sun to one-half its normal value.
Increase the separation between the earth and the sun to four times its normal value.

part A was:

Consider the earth following its nearly circular orbit (dashed curve) about the sun. The earth has mass mearth=5.98

Respuesta :

sebasacevedop

Answer:

Reduce the mass of the earth to one-fourth its normal value.

Reduce the mass of the sun to one-fourth its normal value.

Reduce the mass of the earth to one-half its normal value and the mass of the sun to one-half its normal value.

Explanation:

Every particle in the universe attracts any other particle with a force that is directly proportional to the product of its masses and inversely proportional to the square of the distance between them. So, in this case we have:

[tex]F=\frac{Gm_Em_S}{d^2}[/tex]

If [tex]m'_E=\frac{m_E}{4}[/tex]:

[tex]F'=\frac{Gm'_Em_S}{d^2}\\F'=\frac{G(\frac{m_E}{4})m_S}{d^2}\\F'=\frac{1}{4}\frac{Gm_Em_S}{d^2}\\F'=\frac{1}{4}F[/tex]

If [tex]m'_S=\frac{m_S}{4}[/tex]

[tex]F'=\frac{Gm_Em'_S}{d^2}\\F'=\frac{Gm_E(\frac{m_S}{4})}{d^2}\\F'=\frac{1}{4}\frac{Gm_Em_S}{d^2}\\F'=\frac{1}{4}F[/tex]

If [tex]m'_E=\frac{m_E}{2}[/tex] and [tex]m'_S=\frac{m_S}{2}[/tex]:

[tex]F'=\frac{Gm'_Em'_S}{d^2}\\F'=\frac{G(\frac{m_E}{2})(\frac{m_S}{2})}{d^2}\\F'=\frac{1}{4}\frac{Gm_Em_S}{d^2}\\F'=\frac{1}{4}F[/tex]

Otras preguntas