5.72. Model: We will represent the widget as a particle. Visualize:
Please refer to Figure CP5.72. Solve: (a) There are only two forces on the widget: the normal force of the table and its weight force. (b) Newton’s second law along the y-axis is
( Fnet ) y = ny + w y = ny − mg = may ⇒ ny = m(ay + g) We know what the ay-vs-t graph looks like. To get the ny-vs-t graph, we need to add gy to the graph, which amounts to shifting the whole graph up by 9.8 m/s2, and multiply by m = 5 kg. (c) The normal force is negative for t > 0.75 s. Physically, this means that the normal force is pointed in the downward direction. In other words, the table is pulling down on the widget rather than pushing up on the widget. It can do this because the widget is glued to the table rather than simply sitting on the table. (d) The apparent weight is a maximum at t = 0 s, when the upward acceleration is maximum. (e) The apparent weight is zero at t = 0.75 s when ay = –9.8 m/s2 = –g. (f) If not glued down, the widget will fly off the table at t = 0.75 s, the instant at which its apparent weight becomes zero. The table is accelerating in the negative direction so quickly after t = 0.75 s that the widget can stay on only if the table pulls downward on it. That is the significance of the negative value for ny. If the widget is not glued down, the largest downward acceleration it can achieve is the free fall acceleration.