Answer:
a) m =589.734kg
b) n = 8 people (rounded down)
Step-by-step explanation:
The first step is to calculate the maximum load after safety considerations ([tex]T_{max}[/tex]
Since we know that the maximum tension the cables can withstand is 19500N (or 19.5kN). To calculate ([tex]T_{max}[/tex] we multiply this value by [tex]\frac{2}{3}[/tex] (as per the given safety consideration.
Hence
[tex]T_{max} = \frac{2}{3} (19500) \\ T_{max} = 13000N[/tex]
a) Now to find the maximum load in kgs, we use the following formula
[tex](m_{0} + m)(g + a) = T_{max}[/tex]
Where
[tex]m_{0}[/tex] = mass of elevator
[tex]m[/tex] = maximum load
[tex]g[/tex] = acceleration due to gravity
[tex]a[/tex] = maximum acceleration of elevator
Inputting the values and solving
[tex]m_{0} + m)(g + a) = T_{max}\\ (490 + m)(9.8 + 2.24) = 13000\\ 12.04m = 7100.4\\ m = 589.734kg[/tex]
Hence the maximum load is m =589.734kg
b) To find the number of people (n) we divide the value of m by 70kg
n = 589.734 / 70
n = 8.42 or 8 people
