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Pick an isolated system for the following scenarios while including the fewest number of objects as possible. a. A satellite in orbit around the Earth b. An airplane in flight c. A truck driving along the road d. A person jumping
(a)
The isolated system including the fewest number of objects as possible for the scenario of a satellite in orbit around the earth.
Answer to Problem 1PQ
The earth and satellite are an isolated system by assuming gravitational force due to other objects such as sun are negligible and drag force is negligible.
Explanation of Solution
An isolated system consists of two or more objects in which system’s energy is only converted or changed from one form to another. For an isolated system, energy transfer into or out of the system is not possible. An isolated system is not affected by net external forces that change the momentum of the system. The source of external force originates from a source other than two objects of the system.
Consider a satellite in orbit around the earth. The forces acting on satellite and earth are the gravitational force of attraction of the sun, of the moon, and the drag forces in atmosphere. The distance from sun or moon to earth’s atmosphere is very large compared to distance between the satellite and earth and at the top atmosphere drag force is less, so that neglecting these gravitational attractive forces and drag force will not influence momentum of the system. Centripetal force necessary for orbital motion of a satellite is provided only by earth. All these indicate that satellite and earth form an isolated system.
Conclusion:
The earth and satellite is an isolated system by assuming gravitational force due to other objects such as sun are negligible and drag force is negligible.
(b)
The isolated system including the fewest number of objects as possible for the scenario of an airplane in flight.
Answer to Problem 1PQ
The airplane in flight, earth’s atmosphere, and earth form an isolated system.
Explanation of Solution
An isolated system consists of two or more objects so that momentum of the system is not altered by any external forces. An airplane itself cannot be considered as an isolated system since air drag alters its momentum. Gravitational attraction of earth also affects the motion of the airplane.
Thus, the airplane along with the earth and earth’s atmosphere form an isolated system. No other external forces affect the total momentum of the system. Total energy of this system will be always constant.
Conclusion:
Therefore, the airplane in flight, earth’s atmosphere, and earth form an isolated system.
(c)
The isolated system including the fewest number of objects as possible for the scenario of a truck driving along the road.
Answer to Problem 1PQ
The truck, the road, surrounding air, and earth form an isolated system.
Explanation of Solution
A truck itself driving along the road cannot be considered as an isolated system. Motion of the truck is affected by the surrounding air, frictional force, and gravitational attraction. Since truck is affected by external forces, it cannot be an isolated system.
The truck along with the surrounding air, road, and earth form an isolated system. The total energy of this system is not affected by any other external force.
Conclusion:
Therefore, the truck, the road, surrounding air and earth form an isolated system.
(d)
The isolated system including the fewest number of objects as possible for the scenario of a person jumping.
Answer to Problem 1PQ
A jumping person, the floor, and earth form an isolated system.
Explanation of Solution
According to newton’s third law every action is associated with equal and opposite reaction. A person can jump since he is being acted upon by a force equal to the force he exerts on the floor. The person returns to original place by gravitational attraction of earth.
Total energy of the system consisting of person, earth and floor is always constant. No energy is transferred into or out of the system. Thus, the isolated system consists of that person, earth and the floor.
Conclusion:
Therefore, a jumping person, floor, and earth form an isolated system.
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