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Question: The mass of lift is \(2000\,kg\). When the tension in the supporting cable is \(28000\,N\), then its...

The mass of lift is 2000 kg2000\,kg. When the tension in the supporting cable is 28000 N28000\,N, then its acceleration is
A) 14 m s−214\,m\,{s^{ - 2}}
B) 30 m s−230\,m\,{s^{ - 2}}
C) 4 m s−24\,m\,{s^{ - 2}}
D) 40 m s−240\,m\,{s^{ - 2}}

Explanation

Solution

Tension is a reaction force. It is a part of an action reaction pair of force, with action force in our question being produced by mass. We just need to equate all the forces in the correct manner to get the result. Assume net acceleration and equate it with balancing forces.

Complete step by step answer:
We can see the information given in the Question in the following diagram:

As we can see in the figure the lift is acted upon by two forces. One is due to the tension that is produced in the cable on which lift is hung and other force towards the ground (opposite to direction of tension) which is the weight of lift. As the lift is still accelerating or in motion,it means the net effect of both these forces is not zero. So let us assume the net acceleration with which lift is accelerating =a m s−2 = a\,m\,{s^{ - 2}}
Balancing both the forces will give,
F=mg−TF = mg - T
Where, TT = tension in cable = 28000 N
As the net acceleration of lift is given by a, we can write above equation as:
F=ma=mg−TF = ma = mg - T
ma=mg−Tma = mg - T
Substituting values of variables from the question will give,
2000×a=(2000×10)−280002000 \times a = \left( {2000 \times 10} \right) - 28000
Evaluating above equation will give us net acceleration:
a=−4 m s−2a = - 4\,m\,{s^{ - 2}}
As acceleration is a vector quantity and the negative sign denotes that the acting tension force is more than the weight of lift, hence lift will be pulled by tension force upwards towards itself with acceleration of 4 m s−24\,m\,{s^{ - 2}}.

Therefore, option (C) is correct.

Note: Force, velocity, acceleration and displacement are all vector quantities so their negative sign represents the direction of their action. Tension is a reactive force hence if an object remains suspended without movement in any direction, tension can be considered equal to net downward force (unless any other force is acting in upward direction).