John is standing on a weighing machine installed in a lift. It shows a reading of when the lift is at rest.
What will happen to the reading of the machine if the lift starts accelerating downward?
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Relevant wiki: Newton's Second Law
Although the weighing machine displays the reading in kilograms, it does not measure the mass. but the force by which it is being pressed.
When the lift starts accelerating downward, it is equivalent to the gravity in the lift becoming weaker. As a result, John does not press against the machine as hard, and the reading of the machine decreases.
This can also be seen using Newton's second law of motion. Let the mass of John be m . His weight is m g . When he is rest in the lift, the machine exerts normal force N upwards on John. The machine shows this reading N . Since he is not accelerating, using Newton's second law of motion, m g − N = 0 .
When John is accelerating downwards with acceleration a , the equation of motion is m g − N = m a . The normal force now is N = m g − m a , which is less than m g . We see that the reading of the machine reduced.