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?

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 (

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

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

Where

= mass of elevator

= maximum load

= acceleration due to gravity

= maximum acceleration of elevator

Inputting the values and solving

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

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!