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

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 ($T_{max}$

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 $\frac{2}{3}$ (as per the given safety consideration.

Hence

$T_{max} = \frac{2}{3} (19500) \\ T_{max} = 13000N$

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