If the elevator ascended with constant speed the scale would read the same weight as if the elevator was at rest. However, if the elevator ascends with acceleration the scale will read a greater “weight” and if it descends with acceleration the “weight” will be lower. If it is at rest, the scale will indicate the value of the weight (gravitational force). Observe that the scale will read a different “weight” depending on the acceleration of the elevator. If the elevator is at rest the acceleration of the girl is zero, so the projection of Newton’s second law on the y-axis will be:Īnd the magnitude of the normal N 21 for this case is: If the elevator descends with an acceleration of the same magnitude but opposite direction as in the previous scenario, Newton’s second law is the same, but the projection on the y-axis changes, since now the acceleration has a negative projection on this axis:įrom equation (2) we can isolate the magnitude of the normal N 21 in this scenario: This is the force that the scale will read. Note that, although we have not explicitly represented the vertical axis in the drawing, the unit vector j associated with the observer O indicates the positive direction of that axis.įrom equation (1) we can isolate the magnitude of the normal N 21: With respect to the inertial observer, the girl ascends with the same acceleration as the elevator, so Newton’s second law is: In the following figure are represented the forces that act on the girl: So we will calculate the latter using Newton’s second law. On the other hand, the normal that the girl does on the scale ( N 12) is the normal reaction of the scale on the girl N 21 (Newton’s third law). Therefore, the girl’s weight will be applied to her, not to the scale. The weight is the gravitational force that the Earth exerts on the bodies that are close to its surface. In the statement of the problem the word weight has been quoted because what the scale really measures is the normal force that the girl does on it. Thanks!įirst we will solve the problem with respect to an inertial observer O (resting on the ground).

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