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A woman stands on a scale in a moving elevator. Her mass is 60.0 kg, and the elevator’s mass is 815 kg. Starting from rest, the elevator accelerates upward. During the acceleration, there is a tension of 9410 N in the elevator’s hoisting cable. What does the scale read during the acceleration ?

Respuesta :

lcmendozaf

Answer:

65.81kg

Explanation:

From a forces diagram of the whole elevator:

[tex]T - (m_w+m_e)*g=(m_w+m_e)*a[/tex]   Solving for a we get the acceleration of both the woman and the elevator:

[tex]a=\frac{T-(m_w+m_e)*g}{(m_w+m_e)} =0.95m/s^2[/tex]

Nw, the forces acting on the woman are these:

[tex]N - m_w*g=m_w*a[/tex]   Solving for N:

N = 645N (using g=9.8)    This value divided by the gravity gives us the reading on the scale:

[tex]Scale = \frac{645N}{9.8m/s^2}=65.81kg[/tex]

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