AQA M1 2010 January — Question 6

Exam BoardAQA
ModuleM1 (Mechanics 1)
Year2010
SessionJanuary
TopicNewton's laws and connected particles

6 A small train at an amusement park consists of an engine and two carriages connected to each other by light horizontal rods, as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{fe8c1ea4-cf4d-4741-8af5-03e8c2c88559-4_190_1038_420_493} The engine has mass 2000 kg and each carriage has mass 500 kg . The train moves along a straight horizontal track. A resistance force of magnitude 400 newtons acts on the engine, and resistance forces of magnitude 300 newtons act on each carriage. The train is accelerating at \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
  1. Draw a diagram to show the horizontal forces acting on Carriage 2.
  2. Show that the magnitude of the force that the rod exerts on Carriage 2 is 550 newtons.
  3. Find the magnitude of the force that the rod attached to the engine exerts on Carriage 1.
  4. A forward driving force of magnitude \(P\) newtons acts on the engine. Find \(P\).