A
15-kg block is on a ramp which is inclined at 20° above the horizontal.
It is connected by a string to a 19-kg mass which hangs over the top
edge of the ramp. Assuming that frictional forces may be neglected, what
is the downward acceleration of the 19-kg block?

The one that hangs over the ramp is pulled straight down by gravity, so F = m g = 19 * 9.81 = 186.39 N. For the one on the ramp, you need to decompose the forces. The force along the ramp is m g sin( 20° ) = 15 * 9.81 * sin( 20° ) = 50.3 N. This force works in the opposite direction of the other force, so the resulting force is 136.1 N. This force works on both blocks, so the acceleration is a = F / m_tot = 136.1 / (19 + 15) =