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Bathroom scales read the normal force that is exerted against the floor. What would a scale read when a 100 kg man is in an elevator accelerating upward at 1.2 m/s2? What would it read when the man is accelerated downward at 1.8 m/s2?

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Answer:

a

When the lift is moving upward   [tex]F = 1120 \ N[/tex]

b

When the lift is moving downward   [tex]F = 820 \ N[/tex]

Explanation:

From the question we are told that

     The mass of the man is [tex]m = 100 \ kg[/tex]

     The upward acceleration is  [tex]a_u = 1.2 \ m/s^ 2[/tex]

     The downward acceleration is  [tex]a_d = 1.80 \ m/s^2[/tex]

Generally the force which the scale will read  when the man is moving downward is according to Newton second law represented as  

      [tex]F + mg = ma[/tex]

        [tex]F = m (g - a_d)[/tex]

Here [tex]g = 10 m/s^2[/tex]

=>     [tex]F = 100 (10 - 1.8)[/tex]

=>     [tex]F = 820 \ N[/tex]

Generally the force which the scale will read  when the man is moving upward  is according to Newton second law represented as  

       [tex]F - mg = ma[/tex]

        [tex]F = m (g + a_u)[/tex]

Here [tex]g = 10 m/s^2[/tex]

=>     [tex]F = 100 (10 + 1.2)[/tex]

=>     [tex]F = 1120 \ N[/tex]

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