Question

The mass of a lift is $500\;kg$. What will be the tension in its cable when it is going up with an acceleration of $2.0m/s^2$?

Answer 1

Hint: We know that tension is the action-reaction pair force which is acting on the cables here. And it is the opposite of compression. To solve this question, we can begin by drawing the free body diagram of the lift and the forces acting on it and then find its tension.

Complete step-by-step solution:
Tension is a constant force which acts on the connecting medium like a rope or cable as discussed here. This is majorly a pulling force which tries to maintain the net force acting on the object. It is generally given as the product of mass of the given object and the sum of the acceleration and gravitational force acting on the body at any given time. i.e. mathematically expressed as $T-mg=ma$
It arises due to Newton's third law, that every action which is the gravitational force acting on the lift has an equal and the opposite reaction, which is the tension of the cable and the force due to upward acceleration.
Consider the following situation, where the lift of weight $m=500\;kg$ is pulled upward by a cable with an acceleration of $a=2m/s^2$. Then we also know that acceleration due to gravity also acts on the lift. Then consider the free body diagram as shown below,

Then applying the formula, we have
$\implies T=500(10+2)$
$\therefore T=6000N$
Thus the required answer is $6000\;N.$

Note:The tension on the cable is a non-negative physical quantity acting in the one dimension. If there are no kinks in the cable or its similar material which holds a heavy object, then the tension is equal to the magnitude of the force acting on the other end of the cables.