Second Law: Motion under Same Force

Newton's laws can be applied to bodies at rest and bodies in motion. Newton's first law is applied to bodies in equilibrium, whereas the second law applies to accelerating bodies. To study accelerating bodies, first, the directions and magnitudes of acceleration and the applied forces are determined. Then, the free-body diagram is constructed, and Newton's second law is applied, considering the components of the forces in the x and y directions.

Let's imagine a person is standing on a weighing scale in an elevator. How much will the scale reading change if the elevator accelerates upward? In this case, the scale feels an upward force (ma) in addition to the downward force from gravity (mg). Therefore, the scale shows an increased reading when the elevator accelerates upward. This means that the scale is pushing up on the person with a force greater than their weight, as it has to do so in order to accelerate them upward. Therefore, the greater the acceleration of the elevator, the greater the scale reading. On the other hand, when an elevator accelerates downward, there is an additional downward force (ma) with the downward force from gravity (mg),and so the scale reading is less than the weight of the person. If a constant downward velocity is reached, the scale reading once again becomes equal to the person's weight. Further, if the elevator is in free fall and accelerating downward at g, then the scale reading is zero, and the person experiences weightlessness.

This text is adapted from Openstax, University Physics Volume 1, Section 6.1: Solving Problems with Newton's Laws.