Question

When you weigh yourself on good old terra firma (solid ground), your weight is 142 lb. In an elevator your apparent weight is 121 lb. What are the direction and magnitude of the elevator’s acceleration?

Answer 1

Answer:$1.45 m/s^2$

Explanation:

weight $=142 lb\approx 64.326 kg$

Apparent $=121 lb\approx 54.813 kg$

Apparent weight is decreasing i.e. Elevator is going downward

Apparent weight is given by $m(g-a)=54.813\times 9.81=537.71 N$

$mg=64.326\times 9.81=631.03 N$

631.03-ma=537.71

ma=93.32

$a=\frac{93.32}{64.326}$

$a=1.45 m/s^2$

Elevator is going downward with acceleration of $1.45 m/s^2$

Answer 2

The weight in a moving elevator is increased or reduced depending on the direction and magnitude of the elevator's acceleration

The direction and magnitude of the elevator's acceleration are; downwards, 4.758 ft./s²

Reason:

Given parameter are;

Weight of person in the elevator = 142 lb

Apparent weight as the elevator moves = 121 lb

Required:

The direction and magnitude of the elevator's acceleration

Solution:

The sum of forces acting is given by the change in weight as follows;

The apparent weight of the person = m·(g + a) = 121 lb

The weight of the person = m·g = 142 lb

Given that the apparent weight < Actual weight, we write;

The apparent weight of the person = m·(g - a) = 121 lb

• m·(g - a) - m·g  = 121 lb - 142 lb = -21 lb

m·(g - a) - m·g = m·a

∴ -m·a = -21 lb

$-a = -\dfrac{21}{m} \ lb$

$a = \dfrac{21}{m} \ lb$

$m = \dfrac{142 \, lb}{g}$

Therefore;

• $a = \dfrac{21 \, lb}{\dfrac{142 \, lb}{g} \ } = \dfrac{21 \, lb}{{142 \, lb}} \times g$

Acceleration due to gravity, g ≈ 32.1740 ft./s²

• $a = \dfrac{21 \, lb}{{142 \, lb}} \times g = \dfrac{21 \, lb}{{142 \, lb}} \times 31.1740 \, ft./s^2 \approx 4.758 \ ft./s^2$

Therefore, the magnitude acceleration of the elevator is a ≈ 4.758 ft./s²

Direction of the elevator acceleration vector:

The positive sign of the acceleration of the elevator is the same as the positive sign of gravity acceleration, therefore, the elevator is moving in the direction of gravity, which is downwards

Learn more here:

https://brainly.com/question/20581636