# The cable holding an elevator would break if the tension in it exceeds 25000N. If the 480 kg elevator carries a load limit of 24 passengers (ave mass is 70kg per person) what is the max possible upward acceleration of the elevator without breaking cable?

Apr 14, 2017

$a = 1.76 m {s}^{-} 2$

#### Explanation:

The resultant upwards force on the lift is linked to its acceleration through Newton's 2nd law:

$\text{Tension - weight= ma}$

In this case, total mass is

$480 + 24 \cdot 70 = 2160 k g$
So
#weight =mg=2160*.9.81=21,190N

at breaking point:

$25000 - 21190 = 2160 \cdot a$

Solving gives $a = 1.76 m {s}^{-} 2$