Question

A person who weighs 150 lbs (672 N) when standing still. He observed that he weighs 225 lbs (1008N) on an elevator moving upward. What is the acceleration of the elevator

Answer 1

Step-by-step explanation:

Given:

Force of the person, Fp = 672 N

Force in the elevator, Fe = 1008 N

Fp = mass × g

Fe = mass × (a + g)

Summation of forces = 0

Fp - Fe = 0 (elevator going upward)

Fp = Fe

Fp/a = Fe/(a + g)

672/9.8 = 1008/(a + 9.8)

672a + 6585.6 = 9878.4

a = 3292.8/672

= 4.9 m/s^2

Answer 2

acceleration of elevator =4.91
`m/s^(2)`

Step-by-step explanation:

Consider the normal force acting on you from the elevator:

N = mg if the elevator is at rest or moving at constant velocity

N = mg + ma if the elevator has an upward acceleration

N = mg - ma if the elevator has a downward acceleration

The normal force is equal to your apparent weight. So, you actually feel a little heavier than usual when the elevator accelerates upward, and lighter than usual when the acceleration is down. In more extreme situations this is much more obvious.

What is the acceleration of the elevator;

N = mg + ma if the elevator has an upward acceleration

Normal force(N)=1008N

mg=672N= Force,when elevator is at rest or moving at constant velocity

mass of the person=m kg

acceleration of the elevator= a
`m/s^(2)`

we can find the mass of the person;

F=mg(where g is acceleration due to gravity 9.81
`m/s^(2)`)

672=m*9.81

m=672/9.81

mass=68.5kg

therefore;

N = mg + ma

1008=672+68.5a

68.5a=1008-672

a=336/68.5

acceleration of elevator =4.91
`m/s^(2)`