Work, Power and Energy
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Question : 5
Total: 30
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 earthin 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 figure (i) the man walks 2 m carryingmass of 15 kg on his hands. In figure (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 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 earthin 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 figure (i) the man walks 2 m carryingmass of 15 kg on his hands. In figure (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?
Solution:
(a) When the casing burn up, its mass decreases due to this total energy of the rocket decreases because total energy of rocket in flight depends on its mass. Hence heat energy required for burning is obtained from the rocket itself and not from the atmosphere.
(b) This is because gravitational force is conservative force. Work done by the gravitational force of the sun over a closed path in every complete orbit of the comet is zero.
(c) When the artificial satellite orbiting the earth comes closer and closer to earth, its potential energy decreases. As sum of potential energy and kinetic energy is constant, therefore, K.E. of satellite and hence its velocity goes on increasing. However, total energy of the satellite decreases a little on account of dissipation against atmospheric resistance.
(d) In figure (i), force is applied on the mass, by the man in vertically upward direction but distance is moved along the horizontal
∴ θ = 90 °
W = F s cos 90 ° = Zero .
In figure (ii), force is applied along the vertical and the distance moved is also along the vertical.
Therefore,θ = 0 °
W = F s cos θ = m g × s cos 0 °
W = 15 × 9.8 × 2 × 1 = 294 joule
∴ Work done is greater in 2nd case.
(b) This is because gravitational force is conservative force. Work done by the gravitational force of the sun over a closed path in every complete orbit of the comet is zero.
(c) When the artificial satellite orbiting the earth comes closer and closer to earth, its potential energy decreases. As sum of potential energy and kinetic energy is constant, therefore, K.E. of satellite and hence its velocity goes on increasing. However, total energy of the satellite decreases a little on account of dissipation against atmospheric resistance.
(d) In figure (i), force is applied on the mass, by the man in vertically upward direction but distance is moved along the horizontal
In figure (ii), force is applied along the vertical and the distance moved is also along the vertical.
Therefore,
∴ Work done is greater in 2nd case.
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