Acceleration of an elevator with different lectures of the weighing scale (7068)

, por F_y_Q

A person of mass 70 kg stands on a weighing scale in an elevator which is moving and observes different lectures on it. Determine the acceleration of the elevator and if it is moving up, down, accelereting, breaking or not moving if the values of the scale are: a) 66 kg, b) 74 kg and c) 70 kg.


SOLUCIÓN:

Weight and normal force have opposite sense and next equation is obeyed:

p - N = m\cdot a\ \to\ \color[RGB]{2,112,20}{\bm{a = \frac{(m - m^{\prime})\cdot g}{m}}}

Just substitute the values and calculate the acceleration in each case:

a)

a = \frac{(70 - 66)\ \cancel{kg}\cdot 9.8\ \frac{m}{s^2}}{70\ \cancel{kg}} = \fbox{\color[RGB]{192,0,0}{\bm{0.56\ \frac{m}{s^2}}}}


The elevator is moving down.

b)

a = \frac{(70 - 74)\ \cancel{kg}\cdot 9.8\ \frac{m}{s^2}}{70\ \cancel{kg}} = \fbox{\color[RGB]{192,0,0}{\bm{- 0.56\ \frac{m}{s^2}}}}


The elevator is moving up.

c)

a = \frac{(70 - 70)\ \cancel{kg}\cdot 9.8\ \frac{m}{s^2}}{70\ \cancel{kg}} = \fbox{\color[RGB]{192,0,0}{\bm{0\ \frac{m}{s^2}}}}


The elevator is not moving.