1 A winch operates by means of a force applied by a rope. The winch is used to pull a load of mass 50 kg up a line of greatest slope of a plane inclined at \(60 ^ { \circ }\) to the horizontal. The winch pulls the load a distance of 5 m up the plane at constant speed. There is a constant resistance to motion of 100 N . Find the work done by the winch.
\includegraphics[max width=\textwidth, alt={}, center]{f14ab5b6-f9eb-46a5-b5a6-3d34433313c6-03_585_611_258_765} Two particles \(A\) and \(B\) have masses \(m \mathrm {~kg}\) and 0.1 kg respectively, where \(m > 0.1\). The particles are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley and the particles hang vertically below it. Both particles are at a height of 0.9 m above horizontal ground (see diagram). The system is released from rest, and while both particles are in motion the tension in the string is 1.5 N . Particle \(B\) does not reach the pulley.

1. Find \(m\).
2. Find the speed at which \(A\) reaches the ground.