Weight Change in a Moving ElevatorDate: 12/25/2003 at 18:26:22 From: navkiran Subject: Weight in a moving elevator Why does a person weigh less when coming down the elevator than going up and more when going up than coming down? I think it's because of gravity, but what else is going on? Date: 12/25/2003 at 21:18:24 From: Doctor Rick Subject: Re: Weight in a moving elevator Hi, Navkiran. It's not true that a person weighs less when coming down an elevator than when going up. You weigh less at the BEGINNING of a trip down than at the BEGINNING of a trip up, and MORE at the end of a trip down than at the end of a trip up. At the beginning of a trip down, the elevator is ACCELERATING downward. Soon it reaches a steady speed, and your weight becomes normal. Then it DECELERATES downward (which is the same as accelerating upward) as it comes to a stop at the final floor. Likewise, when going up the elevator first accelerates upward, then reaches a steady speed upward, and finally decelerates to a stop. If you stand on a scale in an elevator, there are two forces acting on you: the downward force of gravity, which is constant (for the purposes of this discussion), and the upward force of the scale on your feet. When you are stationary or when you are moving at a constant speed, these forces are equal and opposite and the scale shows your correct weight. But when you are accelerating up or down, the effect of that acceleration changes the net force and the scale shows a different weight. Net force is calculated by mass (your actual weight) times acceleration and is written as 'ma'. Thus, to pick one case, at the beginning of a trip up in the elevator, you are accelerating upward with acceleration "a". The vertical force equation is N - mg = ma where N is the upward normal force of the scale and -mg is the downward gravitational force. We can solve for N: N - mg = ma N = mg + ma N = m(g + a) The scale measures the force N, dividing it by g (gravity) to read in units of mass (pounds in this example): N/g = m(g + a)/g = m(1 + a/g) = m + ma/g You can see that the scale reads higher than your normal "weight" m because "a" is positive (m and g are always positive). On the other hand, at the beginning of a trip down in the elevator, the scale reads lower than your normal "weight" because "a" is negative (accelerating downward). I have shown why you weigh less at the beginning of a trip down in the elevator than at the beginning of a trip up. If you have questions about what I've said, I'll be happy to answer them. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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