Question

Your engineering firm is asked to specify the maximum load for the elevators in a new building: Each elevator has mass 490 kg when empty and maximum acceleration 2.24 m/s2. The elevator cables can withstand a maximum tension of 19.5 kN before breaking. For safety, you need to ensure that the tension never exceeds two-thirds of that value. What do you specify for the maximum load? How many 70-kg people is that?

Answer 1

a) m =589.734kg

b) n = 8 people (rounded down)

Explanation:

The first step is to calculate the maximum load after safety considerations (
`T_(max)`

Since we know that the maximum tension the cables can withstand is 19500N (or 19.5kN). To calculate (
`T_(max)` we multiply this value by
`(2)/(3)` (as per the given safety consideration.

Hence

`T_(max) = (2)/(3) (19500) \\ T_(max) = 13000N`

a) Now to find the maximum load in kgs, we use the following formula

`(m_(0) + m)(g + a) = T_(max)`

Where

`m_(0)` = mass of elevator

`m` = maximum load

`g` = acceleration due to gravity

`a` = 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`

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