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 (![T_{max}](https://tex.z-dn.net/?f=T_%7Bmax%7D)
Since we know that the maximum tension the cables can withstand is 19500N (or 19.5kN). To calculate (
we multiply this value by
(as per the given safety consideration.
Hence
![T_{max} = \frac{2}{3} (19500) \\ T_{max} = 13000N](https://tex.z-dn.net/?f=T_%7Bmax%7D%20%3D%20%5Cfrac%7B2%7D%7B3%7D%20%2819500%29%20%5C%5C%20T_%7Bmax%7D%20%3D%2013000N)
a) Now to find the maximum load in kgs, we use the following formula
![(m_{0} + m)(g + a) = T_{max}](https://tex.z-dn.net/?f=%28m_%7B0%7D%20%2B%20m%29%28g%20%2B%20a%29%20%3D%20T_%7Bmax%7D)
Where
= mass of elevator
= maximum load
= acceleration due to gravity
= maximum acceleration of elevator
Inputting the values and solving
![m_{0} + m)(g + a) = T_{max}\\ (490 + m)(9.8 + 2.24) = 13000\\ 12.04m = 7100.4\\ m = 589.734kg](https://tex.z-dn.net/?f=m_%7B0%7D%20%2B%20m%29%28g%20%2B%20a%29%20%3D%20T_%7Bmax%7D%5C%5C%20%28490%20%2B%20m%29%289.8%20%2B%202.24%29%20%3D%2013000%5C%5C%2012.04m%20%3D%207100.4%5C%5C%20m%20%3D%20589.734kg)
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