Question

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?

Answer 1

`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`