Apparent weight

In an elevator moving at constant velocity, we seem to have our normal weight. However, when the eleva­tor accelerates upward we seem to weigh more, and when it accelerates down­ward we seem to weigh less. Our true weight (W = m g ) does not depend on the acceleration of the elevator, but our apparent weight does.

The magnitude of the apparent weight of a body is the magnitude of the resultant force exerted on it by a supporting surface.

When an object is placed on a scale, the reading is the magnitude of the normal force between the object and the pan. This normal force is a measure of the apparent weight.

FIGURE 3.10

Figure 3.10 illustrates the forces acting on the object and the two possible directions of the acceleration. In either case the vector form of the second law is N + m g = m a. When the velocity is constant, N = mg: The apparent weight is equal to the true weight. If the acceleration is upward, as in Fig. 3.10 a, we have N - mg = ma and so N = m(g + a): The apparent weight is greater than the normal weight. When the acceleration is downward, as in Fig.3.10 b, we have mg − N = ma and so N = m(g − a): The apparent weight is less than the normal weight.

If the supporting cables were to break, the elevator would be in free-fall, which means a = g and so N = 0. The object would be apparently weightless. In this condition, the object would "float" in the elevator. The condition of apparent weightlessness occurs when an object is in free-fall. If you jump up from the ground, you are apparently weightless while you are in the air.

Дата добавления: 2014-01-05