Essential University Physics: Volume 1 (3rd Edition)

a) $\frac{(m_f-m_s)g}{m_s}$ b) $\frac{m_fa_sh_0}{(m_f-m_s)(g+a_s)}$
a) We know that the net forces must cancel if the spider is to climb without the fly falling. Thus, it follows: $m_sg+m_sa=m_fg\\ m_sa=m_fg-m_sg \\ m_sa=(m_f-m_s)g \\ a=\frac{(m_f-m_s)g}{m_s}$ b) We first find the value of a: $m_sa_s+m_sg=m_fg-m_fa$ $a=\frac{(m_f-m_s)g-m_sa_s}{m_f}$ We know that $y=\frac{1}{2}a_st^2$. We find that the value of $t^2$ is: $t^2=\frac{2h_0}{a_s+a}$ Using substitution, it follows: $h=\frac{m_fa_sh_0}{(m_f-m_s)(g+a_s)}$