- #1

hi im nimdA

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- Homework Statement
- Two point particles, each of mass 100 kg, are initially at rest 1 m apart in outer space. (a) What is their initial acceleration? (b) What are their speeds when their separation is 0.5 m?

- Relevant Equations
- (1) F=G (m1m2)/r^2

(2) F=ma

First, I started with [tex]F_a = m_aa_a=G \frac{m_am_b}{r^2} [/tex] and [tex]F_b = m_ba_b=G \frac{m_am_b}{r^2} [/tex]. Solving for their respective accelerations, I got [tex] a_a=G \frac{m_b}{r^2} = 100G[/tex] and [tex] a_b=G \frac{m_a}{r^2} = 100G[/tex], meaning that the initial acceleration of the two point particles are each [itex] 100G [/itex]. When I tried to do part (b), I realized that their accelerations will keep changing as they get closer to each other, meaning that I can't use the kinematic equations, since they require a constant acceleration. I'm not too sure how to go about solving part (b).

I was thinking maybe [tex]v(r) = \int a(r) dr[/tex] [tex] v(r) = \int_{1}^{0.5} \frac{100G}{r^2} dr[/tex] Thanks for the help

I was thinking maybe [tex]v(r) = \int a(r) dr[/tex] [tex] v(r) = \int_{1}^{0.5} \frac{100G}{r^2} dr[/tex] Thanks for the help