Question

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 v0, and the turntable is independently set in motion to rotate

counterclockwise with an angular speed ω. Neglect the physical dimensions of the train.

Figure 1:

(a) Write down the equations of motion for the radial coordinates of the engine and the

wagon, denoted by r1 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 = r1 − r2 between

the engine and the wagon. Solve the equation and find r(t) subject to the given initial

conditions (assume that ω

2 < 2k/m) (2 MARKS).

(d) Find r(t) if ω

2 > 2k/m. Speculate about what would happen to the train1

in this case,

if the table is infinite in extent (2 MARKS).​

Answer 1

Answer:

Good night

Sweet Dreams

Answer 2

Answer:

maths ka hai

of which class