Concept explainers
Review Question 7.1 Assuming that Earth’s orbit around the Sun is circular, what information do you need to estimate the work done by the Sun on Earth while Earth travels 1000 km? Explain your answer.
The information needed to estimate the work done by the Sun on the Earth while Earth travels
Answer to Problem 1RQ
Solution:
No information is needed because work done by the Sun on the Earth is zero in this case.
Explanation of Solution
Introduction:
Work done by any force is defined as the product of force and the displacement in the direction of the force.
In this question, it is assumed that Earth’s orbit is circular, i.e., Earth’s displacement in the radial direction is zero at every point of the path.
Explanation:
When the orbit is assumed to be circular radius, it is constant at every point of the path, i.e., there is no displacement in the direction of the radius. Since, the Sun is at the center of this circular orbit, so the gravitational force between the Sun and Earth is always towards the center and along the radius.
The equation for the work done is given below.
Here,
In the case of a circular path, the angle between displacement and the force is
When
Conclusion:
Work done by centripetal force in case of circular motion is always zero. In this case, the Earth’s orbit is assumed to be circular, the gravitational force’s direction is always along the radius towards the center, i.e., the Sun. But, displacement along the radius is zero at every point of the path. Hence, the work done is zero.
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