#### Answer

The mass of the cable is 5.0 kg

#### Work Step by Step

Consider the system of the block and the cable. We can find the acceleration of the system.
$a = \frac{v^2-v_0^2}{2x}$
$a = \frac{(4.0~m/s)^2-0}{(2)(2.0~m)}$
$a = 4.0~m/s^2$
Let $m_b$ be the mass of the block. Let $m_c$ be the mass of the cable. We can find the mass of the cable.
$F = (m_b+m_c)~a$
$m_c = \frac{F - m_b~a}{a}$
$m_c = \frac{(100~N) - (20~kg)(4.0~m/s^2)}{4.0~m/s^2}$
$m_c = 5.0~kg$
The mass of the cable is 5.0 kg