Question

A man of weight $80\, kg$ is standing in an elevator which is moving with an acceleration of $6\,m/{{s}^{2}}$ in upward direction. The apparent weight of the man will be $(g=10\,\,m/{{s}^{2}})$ :

• A. 148 N
• B. 128 N
• C. 138 N
• D. None of these

Answer 1

Answer: (B)

128 N

Answer 2

When elevator is moving up, effective acceleration increases.
When man is standing in an elevator going up, with an acceleration a the net force on the man is
$F=mg-R$ From Newtons second law of motion,
the net force on him is
$F = - ma$(downwards)
$\therefore$ $-ma=mg-R$
$\Rightarrow$ $R=mg+ma$
Since, $R=w$ $w=m\,(g+a)$
Given, $m=\frac{80}{10}=8\,kg$,
$g=10\,m/{{s}^{2}},a=6\,m/{{s}^{2}}$
$\therefore$ $w=8\,(10+6)\,w=128\,N$
Note: When elevator is going up, weight of man is greater than the gravity force $mg$.
That is, the man will feel his weight to be increased than in the normal state.