$A$ steam engine of mass $3 \times 10^{4} \text{ kg}$ pulls two wagons,each of mass $2 \times 10^{4} \text{ kg}$,with an acceleration of $0.2 \text{ m s}^{-2}$. Neglecting frictional forces,calculate the:
$(i)$ force exerted by the engine.
$(ii)$ force experienced by each wagon.

(N/A) Given:
Mass of engine $M_{E} = 3 \times 10^{4} \text{ kg}$
Mass of each wagon $M_{w} = 2 \times 10^{4} \text{ kg}$
Acceleration $a = 0.2 \text{ m s}^{-2}$
$(i)$ The total mass being pulled by the engine is $M_{total} = M_{E} + 2M_{w} = 3 \times 10^{4} + 4 \times 10^{4} = 7 \times 10^{4} \text{ kg}$.
The force exerted by the engine is $F = M_{total} \times a = (7 \times 10^{4} \text{ kg}) \times (0.2 \text{ m s}^{-2}) = 1.4 \times 10^{4} \text{ N}$.
$(ii)$ The force experienced by each wagon is the force required to accelerate that specific wagon. For one wagon,$F_{w} = M_{w} \times a = (2 \times 10^{4} \text{ kg}) \times (0.2 \text{ m s}^{-2}) = 0.4 \times 10^{4} \text{ N} = 4000 \text{ N}$.