Question

An elevator manufacturer determines the maximum force acting on ascending passengers should not exceed 110% of a standing passenger's weight on their feet . What would be the minimum time possible according to this manufacturer to rise 10 floors from rest if each floor is 5.00 m apart?

(A) 6.00

(B) 10.0

(C) 19.0

(D) 24.0

Answer 1

Balancing Forces,

$N-mg=ma$

From question,

$N<=\dfrac{110}{100}mg$

Put this value in above equation,

$1.1mg-mg=ma$

$a=0.1g$

Taking acceleration due to gravity, $g=10\space m/s^2$

Total displacement, $s=10\times 5=50\space m$

Initial velocity, $u=0\space m/s$

From Newton's laws of motion,

$s=ut+\dfrac{1}{2}at^2$

$50=\dfrac{1}{2}\times0.1gt^2$

$t=\sqrt{\dfrac{2\times50}{0.1g}}$

$t=\sqrt{\dfrac{100}{0.1\times10}}=10\space s$