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25 March, 08:45

An elevator is moving down at a constant rate of 4 m/s. A person is standing on a scale that says the person weighs 80 N. When it reaches the bottom, it comes to a stop in 2 seconds.

During the stopping process, what is the reading on the scale?

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  1. 25 March, 09:43
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    The reading on the scale is 96.31 N.

    Explanation:

    When the elevator comes to a stop the speed decreases from 4 m/s to 0 m/s.

    This means that it incurs deceleration. We can use the formula below to find out the force that is applied on the person during this deceleration:

    F = mass * acceleration

    Assuming the deceleration is constant, we have the following equation:

    V = U + at

    Where V = Final speed = 0

    U = initial speed = 4

    a = acceleration

    t = time

    Solving, we get:

    0 = 4 + 2a

    a = - 2 m/s^2

    Thus the object decelerates at 2 m/s^2

    The mass of the person = 80 / 9.81 = 8.155 kg

    F = 8.155 * 2

    F = 16.31 N

    Total weight = 80 + 16.31 = 96.31 N (This is the reading on the scale)
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