Question

A railway engine of mass 50tons is pulling a wagon of mass 40tons with a force of 4500N. The resistance force acting is 1N per ton. The tension in the coupling between the engine and the wagon is
A) $1600N$
B) $2000N$
C) $200N$
D) $1500N$

Answer 1

When there is a force applied between two objects, then there act many forces internally and externally in order to get a net motion of the object.

Complete step by step answer:
Step I:
Given resistance force is acting, it is defined as the force which acts in a direction opposite to the velocity of the body.
Another force tension force (T) is also acting in the coupling between the engine and wagon. Tension force is the force that is created by pulling something very tight or any physical or mental strain. This force is equal to the mass of the object and gravitational force.
$T = ma$--------(i)
Where $m$is the mass
$a$is acceleration.

Step II:
Here Newton’s second law is applicable. As per this law, the acceleration of an object produced by the net force is directly proportional to the magnitude of the net force in the same direction as the force and inversely proportional to the mass.

Step III:
Given mass of engine$= 50tons$
Mass of wagon$= 40tons$
Combined mass of engine and wagon,$m = 50 + 40 = 90tons$
Force,$F = 4500N$
Using the equation, $F = ma$--------(ii)
Substituting the values and evaluating acceleration, in equation(ii)
$4500 = 90 \times a$
$a = \dfrac{{4500}}{{90}}$
$a = 50m/{s^2}$

Step IV:
Calculating tension, by substituting the values in equation (i),
$T = 40 \times 50$
$T = 2000N$

The tension force between the engine and the wagon is $2000N$. Hence, Option B is the right answer.

Note:
It is to be noted that tension in the string is independent of the length or the distance between the objects. In other words, tension can also be described as a pair of action-reaction forces acting at the ends of the two objects taken into consideration.