Physics, 04.06.2020 13:09 theactualslash
N experiment is performed in deep space with two uniform spheres, one with mass 27.0 and the other with mass 107.0 . They have equal radii, = 0.10 . The spheres are released from rest with their centers a distance 41.0 apart. They accelerate toward each other because of their mutual gravitational attraction. You can ignore all gravitational forces other than that between the two spheres.
A) When their centers are a distance 26.0 apart, find the speed of the 27.0 sphere.
B) Find the speed of the sphere with mass 107.0 .
C) Find the magnitude of the relative velocity with which one sphere is approaching to the other.
D) How far from the initial position of the center of the 27.0 sphere do the surfaces of the two spheres collide?
Answers: 3
![Gm_1m_2[\frac{1}{r_f} -\frac{1}{r_1} ]=\frac{1}{2} (m_1v_1^2+m_2v_2^2)](/tpl/images/0675/6851/f6d83.png)
![=\frac{1}{2} [m_1v_1^2+m_2[\frac{m_1v_1}{m_2} ]^2]\\\\=\frac{1}{2} [m_1v_1^2+\frac{m_1^2v_1^2}{m_2} ]\\\\=\frac{m_1v_1^2}{2} [\frac{m_1+m_2}{m_2} ]](/tpl/images/0675/6851/96624.png)
![v_1^2=[\frac{2Gm_2^2}{m_1+m_2} ][\frac{1}{r_f} -\frac{1}{r_1} ]](/tpl/images/0675/6851/833ea.png)
![=[\frac{2(6.67\times 10^-^1^1)(107)^2}{27+107} ][\frac{1}{26} -\frac{1}{41}] \\\\=1.6038\times 10^-^1^0\\\\v_1=\sqrt{1.6038\times 106-^1^0} \\\\=1.2664 \times 10^-^5m/s](/tpl/images/0675/6851/62f1d.png)
\\\\=3.195\times 10^-^6m/s](/tpl/images/0675/6851/58d1c.png)
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