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 burningobtained? 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 casing of the rocket burns out due to friction and the heat energy that is required to burn the casting of the rocket comes out of the rocket itself. The fuel of the rocket burns which provides the energy to resist the gravitation force and the air resistance.
As a result, the work is done continuously against the friction. So, the kinetic energy of the rocket simultaneously decreases and the work against the friction reappears as heat energy.
Thus, the rocket expenses the heat energy for burning the casing of the rocket against friction.
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.
As the gravitational force is a conservative force, it means that it remains conserved. So, for a complete orbit that is the closed path travelled around the sun, the net force is zero, and so the work done is also zero.
Thus, the work done by the comet for a complete revolution is zero as the gravitational force is covered for a complete revolution.
c)
An artificial satellite orbiting the earth in very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance, but the net energy of the satellite remains constant.
The total energy remains conserved which is the sum of the potential energy and the kinetic energy. So, as the potential energy decreases due to atmospheric resistance, the kinetic energy increases correspondingly.
Thus, the potential energy decreases and the kinetic energy of the satellite increases.
d)
For the first case, the man walks with the mass in his hands, so the angle between the force applied and the displacement is 90 ° .
The formula to calculate the work done in the first case is,
W 1 = m g s cos θ
Here, the mass of the box is m , the displacement of the body is s , the gravitational acceleration of the box is g and the angle between the force applied and the displacement is θ .
Substitute the values in the above equation.
W 1 = ( 15 ) ( 9.8 ) ( 2 ) cos 90 ° = 294 ( 0 ) = 0 J
Thus, the work done in the first case is 0 J .
The formula to calculate the work done in the second case is,
W = m g s cos θ
Here, the mass of the box is m , the displacement of the body is s , the gravitational acceleration of the box is g and the angle between the force applied and the displacement is θ .
As he walks the same distance pulling the rope behind him, so the angle between the force applied and the displacement is 0 ° .
Substitute the values in the above equation.
W = ( 15 ) ( 9.8 ) ( 2 ) cos 90 ° = 294 ( 1 ) = 294 J
Thus, the work done in the second case is 294 J and the work done in the second case is greater than the first.
a)
The casing of the rocket burns out due to friction and the heat energy that is required to burn the casting of the rocket comes out of the rocket itself. The fuel of the rocket burns which provides the energy to resist the gravitation force and the air resistance.
As a result, the work is done continuously against the friction. So, the kinetic energy of the rocket simultaneously decreases and the work against the friction reappears as heat energy.
Thus, the rocket expenses the heat energy for burning the casing of the rocket against friction.
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.
As the gravitational force is a conservative force, it means that it remains conserved. So, for a complete orbit that is the closed path travelled around the sun, the net force is zero, and so the work done is also zero.
Thus, the work done by the comet for a complete revolution is zero as the gravitational force is covered for a complete revolution.
c)
An artificial satellite orbiting the earth in very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance, but the net energy of the satellite remains constant.
The total energy remains conserved which is the sum of the potential energy and the kinetic energy. So, as the potential energy decreases due to atmospheric resistance, the kinetic energy increases correspondingly.
Thus, the potential energy decreases and the kinetic energy of the satellite increases.
d)
For the first case, the man walks with the mass in his hands, so the angle between the force applied and the displacement is
The formula to calculate the work done in the first case is,
Here, the mass of the box is
Substitute the values in the above equation.
Thus, the work done in the first case is
The formula to calculate the work done in the second case is,
Here, the mass of the box is
As he walks the same distance pulling the rope behind him, so the angle between the force applied and the displacement is
Substitute the values in the above equation.
Thus, the work done in the second case is
