Respuesta :
Answer:
a) 584.39 kg
b) 7
Explanation:
Given;
Mass of the elevator, m = 500 kg
Maximum acceleration, a = 2.25 m/s²
Maximum tension = 19.6 kN
Allowable tension = [tex]\frac{\textup{2}}{\textup{3}}\times\textup{Maximum tension}[/tex] = [tex]\frac{\textup{2}}{\textup{3}}\times\textup{19.6}[/tex]
= 13.067 kN
a)let the maximum load be 'x' Now,
T(max) = mass × acceleration
13.067 kN = ( 500 + x ) × ( g + a ) [maximum acceleration will be when lift moves upward i.e (g + a )]
or
⇒ 13.067 × 10³ N = ( 500 + x ) × ( 9.8 + 2.25 )
or
⇒ 13.067 × 10³ N = ( 500 + x ) × 12.05
or
⇒ 13.067 × 10³ N = 6025 + 12.05x
or
⇒ 13067 - 6025 = 12.05x
or
⇒ 12.05x = 7042
or
⇒ x = 584.39 kg
b) Mass of a person = 75.0 kg
Number of 75.0 kg persons that can be allowed = [tex]\frac{\textup{Maximmum load}}{\textup{Mass of each person}}[/tex]
= [tex]\frac{\textup{584.39}}{\textup{75}}[/tex]
= 7.79
to be on safer side, rounding off to nearest lowest integer i.e 7
