# Answer to Question #21963 in Mechanics | Relativity for rahav

Question #21963
A man weighs himself inside a lift. He weighs 72kg-wt when the lift goes up with a constant acceleration &lsquo;a&rsquo; , while he weighs 69kg-wt when the lift goes down with the same acceleration. The mass of the man is?
1
2013-01-21T07:39:28-0500
According to the second Newton&#039;s law, the force acting on a man when the lift goes up with a constant acceleration is

F1 = M&middot;(g+a), (1)

where M is the mass of a man. From the other side, the force acting on a man when the lift goes down with the same acceleration is

F2 = M&middot;(g-a). (2)

Let&#039;s add equations (1) and (2):

F1 + F2 = M&middot;(g+a) + M&middot;(g-a),

F1 - F2 = M&middot;g + M&middot;a + M&middot;g - M&middot;a,

F1 + F2 = 2&middot;M&middot;g.

Therefore,

M = (F1 + F2) / (2&middot;g)

Taking into account that

F1 = 72[kg-wt] &asymp; 72&middot;g[N]

and

F2 = 69[kg-wt] &asymp; 69&middot;g[N],

we have

M = (72&middot;g[N] + 69&middot;g[N]) / (2&middot;g[m/s&sup2;]) = (72[N] + 69[N]) / (2[m/s&sup2;]) = 70.5[kg].

So, the mass of a man is 70.5 kg.

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