Question

2. A toy train consists of an engine and wagon of equal mass m each, connected by a spring
with spring constant k. The relaxed length of the spring may be considered to be zero. The
train is initially placed at the centre of a horizontal, circular turntable (see Fig. 1), and is
free to move on a radial frictionless track on the turntable. The engine (alone) is now given
an initial (radial) velocity vo, and the turntable is independently set in motion to rotate
counterclockwise with an angular speed w. Neglect the physical dimensions of the train.
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Figure 1:
(a) Write down the equations of motion for the radial coordinates of the engine and the
wagon, denoted by ri and r2 (1 MARK).
(b) Using (a), write down the equation of motion for the radial coordinate R(t) of the centre
of mass (COM) of the train. Solve this equation subject to the given initial conditions
and determine R(t) (2 MARKS).
(c) Using (a), write down the equation of motion for the separation r = ri - r2 between
the engine and the wagon. Solve the equation and find r(t) subject to the given initial
conditions (assume that w2 < 2k/m) (2 MARKS).
(d) Find r(t) if w2 > 2k/m. Speculate about what would happen to the train' in this case,
if the table is infinite in extent (2 MARKS).​

Answer 1

Answer:

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