13 A toy train consists of an engine of mass 0.5 kg pulling a coach of mass 0.4 kg . The coupling between the engine and the coach is light and inextensible. The train is pulled along with a string attached to the front of the engine.
At first, the train is pulled from rest along a horizontal carpet where there is a resistance to motion of 0.8 N on each part of the train. The string is horizontal, and the tension in the string is 5 N .
- Determine the velocity of the train after 1.5 s .
The train is then pulled up a track inclined at \(20 ^ { \circ }\) to the horizontal. The string is parallel to the track and the tension in the string is \(P \mathrm {~N}\). The resistance on each part of the train along the track is \(R \mathrm {~N}\).
- Draw a diagram showing all the forces acting on the train modelled as two connected particles.
- Find the equation of motion for the train modelled as a single particle.
- The acceleration of the train when \(P = 5.5\) is double the acceleration when \(P = 5\).
Calculate the value of \(R\).