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

Answer:

$6.08m/s^2$

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,

$a= \frac{F_{tol}-F_{T}}{M_{tot}}$

$a= \frac{27002-(1700*9.8)}{1700}$

$a=6.08m/s^2$