Answer the following:
A. The casing of a rocket in flight burns up due to friction. At whose expense is the heat energy required for burning obtained? The rocket or the atmosphere?
B. Comets move around the sun in highly elliptical orbits. The gravitational force on the comet due to the sun is not normal to the comet’s velocity in general. Yet the work done by the gravitational force over every complete orbit of the comet is zero. Why?
C. An artificial satellite orbiting the earth in very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance, however small. Why then does its speed increase progressively as it comes closer and closer to the earth?
D. In Fig. 6.13(i) the man walks 2 m carrying a mass of 15 kg on his hands. In Fig. 6.13(ii), he walks the same distance pulling the rope behind him. The rope goes over a pulley, and a mass of 15 kg hangs at its other end. In which case is the work done greater?
A. The heat energy required for burning is obtained at the expense of the rocket. The mass of the rocket is consumed to supply for the loss in total energy of the rocket.
B. Gravitational force is conservative in nature. The work done by a conservative force in a closed cycle is zero. Hence, work done by the gravitational attraction of sun is zero.
C. When the satellite comes closer to the earth, its potential energy decreases (∵ PE = mgh where h is the height of the object from the earth). To maintain constant total energy, the kinetic energy increases and hence velocity increases.
D. Given,
Mass = 15 kg
Displacement, s = 2 m
In figure 1:
Work done, W = F∙s
⇒ W = F×s×cosθ
⇒ W = F×s× cos 90°
⇒ W = 0 (∵ cos 90° = 0)
In figure 2:
Work done, W = F∙s
⇒ W = F s cosθ
⇒ W = m g s cos 0°
⇒ W = 15 kg ×9.8 m s-2× 2 m × 1
⇒ W = 294 J
Hence, more work is done in figure 2.