An elevator has a scale that shows your weight while you are in it. You enter th

Question

An elevator has a scale that shows your weight while you are in it. You enter the elevator on the sixth floor and going down to the ground floor. State whether the scale on the elevator shows your weight (same), more than your weight, more than your weight, or less than your weights in the following instances.

a) The elevator slows down in preparation for stopping at the ground floor . b) the elevator travels downward between floors at a constant speed. c) The elevator starts downward towards the ground floor. d) You get on the elevator on the sixth floor

Explanation / Answer

(a) As the elevator slows down, i.e a reverse force is applied by the elevator, in other words an upward acceleration is introduced. To apply newtonian mechanics we need to make this non-inertial system, back to inertial frame. This is accomplished by introducing a psuedo acceleration downward along the direction of acceleration due to gravity.

hence net g'=g+a or the weighing maching will show an increased weight. as W=Mg' and g'>g

(b) If the elevator travels down at constant speed, then there is no other force apart from acceleration due to gravity. Hence the machine will show same weight.

(c) When elevator starts downward, there is an added accleration downward along with acceleartion due to gravity, again to make the system inertial frame, we have to apply a psuedo acceleration directed upward.

or g'=g-a , i.e g'<g

or in other words the machine will show lesser weight.

Note: If the elevator goes into free fall, i.e a=g , this situation is called the weightless ness condition as Mg-Ma=0 since a=g.

(d) On the sixth floor, the height might( i.e distance from center of the earth) change the value of acceleration due to gravity, but it is insignificant. Hence the weight will be more or less same, as long as the elevator is stationary or moving at constant speed.

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