Understanding Work in Physics
In physics, the term 'work' has a very specific definition. It is not just about exerting effort; it is defined as the product of the component of the force in the direction of motion and the distance moved. Mathematically, work ($W$) is defined as:
$$W = F \cdot d \cdot \cos(\theta)$$
Where:
- $F$ is the magnitude of the force.
- $d$ is the magnitude of the displacement.
- $\theta$ is the angle between the force vector and the displacement vector.
The Problem Statement
The question asks: "The earth moving round the sun in an orbit is acted upon by a force, hence the work must be done on the earth by this force. Do you agree with this statement?"
The Answer
No, we do not agree with this statement.
While it is true that the Earth is acted upon by a gravitational force (the centripetal force provided by the Sun), this force does zero work on the Earth.
Why is the Work Zero?
- Direction of Force: The gravitational force exerted by the Sun on the Earth always acts towards the center of the orbit (the Sun).
- Direction of Motion: The Earth's orbital motion is tangential to the orbit at every point.
- The Angle: Because the velocity vector (tangential) is always perpendicular ($90^\circ$) to the position/force vector (radial), the angle $\theta$ between the force and the displacement is $90^\circ$.
Since $\cos(90^\circ) = 0$, the calculation becomes:
$$W = F \cdot d \cdot \cos(90^\circ) = F \cdot d \cdot 0 = 0$$
Intuition
Work represents the transfer of energy. When a force does positive work, it increases an object's kinetic energy (it speeds up). When it does negative work, it decreases kinetic energy (it slows down). Because the Earth maintains a constant orbital speed (assuming a circular orbit), its kinetic energy does not change. Therefore, no net work is being done on it.