# how to solve probleems related to two bodies connected to a spring by using conservation of linear momentum and energy.how to use reduced mass concept?

SAGAR SINGH - IIT DELHI
879 Points
11 years ago

Dear student,

In such questions apply 2 concepts:

Conservation of energy

Conservation of momentum

36 Points
11 years ago

Dear student,

Given two bodies, one with mass $m_{1}\!\,$ and the other with mass $m_{2}\!\,$, they will orbit the barycenter of the two bodies. The equivalent one-body problem, with the position of one body with respect to the other as the unknown, is that of a single body of mass

$m_\text{red} = \mu = \cfrac{1}{\cfrac{1}{m_1}+\cfrac{1}{m_2}} = \cfrac{m_1 m_2}{m_1 + m_2},\!\,$

The relative acceleration between the two bodies is given by

$a= a_1-a_2 = \left({1+{m_1 \over m_2}}\right) a_1 = {{m_2+m_1}\over{m_1 m_2}} m_1 a_1 = {F_{12} \over m_\text{red}}.$