A train locomotive of mass m0=671 Mg is pulling two railcars, the first of mass

Question

A train locomotive of mass m0=671 Mg is pulling two railcars, the first of mass m1=114 Mg and the second of mass m2=73 Mg, along a horizontal track with acceleration a=0.9 m/s^2.

(i)Derive an algebraic expression for the forward thrust of the locomotive, Fthrust =
(ii)Derive an algebraic expression for the tension in the first connector, T1 =
(iii)Derive an algebraic expression for the tension in the second connector, T2 =
(iv)Derive an algebraic expression for the net force on the first railcar, F1 =

Neglecting the mass of the connectors and any internal friction, determine the magnitudes of
(a) the forward thrust of the locomotive;
(b) the tension in the first connector;
(c) the tension in the second connector;
(d) the net force on the first railcar.

Explanation / Answer

By Newton's second law
Net external force on freee body = Mass of free body * accelerations
a) Taking Locomotive + 2 Railcars as free body
Forward thrust on Locomotive = (Mo + M1 + M2) a = 7.7 x 105 N

b) Taking two railcars as free body, External force is tension in the first connector
hence T1 = ( M1 + M2) a = 1.7 x105 N

c) Taking only second rail car as free body, external force is tension in the second connector,
Hence T2 = M2 * a = 0.7 x105 N

d) Net force of first rail car = Mass of first rail car x acceleration = M1 *a = 105 N
This is also equal to T1 - T2 , as these are the two forces acting on first Railcar in opposite direction.  

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