You may have such an experience inside an elevator: When the elevator accelerates upwards, you weigh more than you actually do, and when the elevator decelerates, you weigh less. To explain this phenomenon, we have to apply Newton's Laws of Motion.

Suppose a person of weight is standing on a weighting machine in an elevator (Fig. 6-4). The weighting machine and the person interact with the action-reaction pair of force and as shown in figure. As discussed before, does not form an action-reaction pair with .

The weighting machine measures the force (=) acting on it, but not the actual weight of the person. It is interesting to see that and are not always the same. We shall analyze the problem in three different cases.

Fig. 6-4 (Left) A man standing on a weighting machine in an elevator. (Right) Free body diagram of the man.

Suppose the elevator is at rest or moving with constant velocity (acceleration ). By Newton's second law, the resultant force acting on the person is zero, i.e.,

,

hence , i.e., the machine gives the true weight of the person. However, if the elevator is accelerating upwards (, take upward direction as positive),

,

so , i.e., the machine gives a reading greater than the true weight of the person. In other words, the person weighs more in the elevator!

Similarly, when the elevator decelerates (),

so and so the person weighs less in the elevator!


 Flash animation: Change in weight of a person inside an elevator

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 Example
 
Fig. 6-5 Free body diagram of the student.

A student of mass 40 kg is now standing on a weighting machine in an elevator (Take ).

  1. What is the acceleration (magnitude and direction) of the student if the reading on the weighing machine is 450 N?
  2. Can we determine the direction of motion of the lift from the reading of the machine alone? Explain your answer.

Solution :

The free body diagram of the student is shown in Fig. 6-5 (take upward direction as positive).

  1. First we have to find the resultant force acting on the student:

    2. (upwards)

    Apply ,

    (upwards)

  2. No. We know the direction of acceleration but not the direction of the velocity. The elevator may be moving upwards with an increasing speed, or moving downwards with a decreasing speed. In both cases, the acceleration points downwards and the student gains weight.
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