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A sign in an elevator states that the maximum occupancy is 16 persons. Suppose safety engineers assume the mass of an average person is 73 kg. The elevator itself has a mass of 532 kg. The supporting cable can tolerate a maximum force of 27002 N. What is the greatest acceleration the elevator's motor can produce without snapping the cable when the elevator is full?

User Ckundo
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1 Answer

1 vote

Answer:


6.08m/s^2

Step-by-step explanation:

We define our values, we know that,


N=16


m_p=73kg


m_e=532kg


F_(tol)=27002N

our total mass is given by,


M_(tot) = N*m_p+m_e


M_(tot) = 73*16+532


M_(tot) = 1700Kg

making summatory in y, we have that


\sum F_y = M_(tot)a


F_T-F_(tol) = M_(tot)a

Re-arrange for a,


a= (F_(tol)-F_(T))/(M_(tot))


a= (27002-(1700*9.8))/(1700)


a=6.08m/s^2

User Bryan Bende
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