the mass of a man standing on a lift is 60kg. what is the weight when he is staying on lift which is moving upward with acceleration 4.9 ms^-2
Answers
The lift is at rest in the third floor. No man is inside the lift. But gravity pulls it down. Still the lift is at rest. How ? This implies that some upward force F is acting on the lift and prevents it's fall. Now a man enters inside the lift. The gravity ( the weight of the man) W pushes the lift down, but concurrently the upward force increases by the amount equal to the weight of the man, and both the lift and the man are at rest. The additional upward force here equals the weight of the man and this force is called apparent weight and = W.
Now suppose that the upward forces F and W (up) ceases to act. Or W + F = 0.
The lift falls freely under gravity. The man also falls freely under gravity. Both move down with an acceleration g. For the man there is no up ward force to prevent his fall. Or the apparent weight is zero. The man feels that he has lost all his weight.
Thus if the lift falls freely under an acceleration g, the man's apparent weight REDUCES to zero.
If there were a small upward force, f , the lift and the man will fall down with an acceleration less than g. The man will feel an apparent weight f. Though not zero it is still less than his weight W.
If there were large upward force, greater than both the weight of the lift and the weight of the man, both will move up with an acceleration say a. The man will feel as if his weight has increased by an amount ma where m is his mass.
If the man moves up or down with constant speed, the man will feel his weight mg , since here the upward force is also mg.
In short, if the man is at rest or if he is moving up or down with uniform speed, a force equal to his weight mg acts upward and his apparent weight is also mg.
If he falls freely under gravity, there is no upward force and his apparent weight is 0.
If he falls with an acceleration less than g say a, the upward force is m (g-a) The apparent weight f reduces to m(g-a).
If he moves up with an acceleration a, the upward force is m(g+a) . The apparent weight increases to m(g+a) .
What will be his apparent weight, if some how, the lift falls with an acceleration greater than g? Think.