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 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}}) $ :
Updated On: Jan 18, 2023
- 148 N
- 128 N
- 138 N
- None of these
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The Correct Option is B
Solution and Explanation
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.
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.
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Concepts Used:
Newtons Laws of Motion
Newton’s First Law of Motion:
Newton’s 1st law states that a body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force acts on it.
Newton’s Second Law of Motion:
Newton’s 2nd law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the object’s mass.
Mathematically, we express the second law of motion as follows:
Newton’s Third Law of Motion:
Newton’s 3rd law states that there is an equal and opposite reaction for every action.