Define work. Write it’s SI unit. Is work scalar or vector?
The correct answer and explanation is:
Work in physics refers to the transfer of energy when a force is applied to an object, causing it to move in the direction of the applied force. Mathematically, work is defined as the product of the force applied to an object and the distance over which the force is applied. It is expressed as: W=F×d×cos(θ)W = F \times d \times \cos(\theta)
Where:
- WW is the work done,
- FF is the force applied,
- dd is the displacement of the object,
- θ\theta is the angle between the direction of the force and the direction of displacement.
SI Unit of Work:
The SI unit of work is the joule (J). One joule is defined as the amount of work done when a force of one newton acts on an object over a displacement of one meter in the direction of the force. Mathematically: 1 J=1 N×1 m1 \, \text{J} = 1 \, \text{N} \times 1 \, \text{m}
Where:
- 1 N1 \, \text{N} (newton) is the unit of force,
- 1 m1 \, \text{m} (meter) is the unit of distance.
Is Work Scalar or Vector?
Work is a scalar quantity. This means it does not have a direction, only a magnitude. Unlike vectors such as force or displacement, which require both magnitude and direction, work only depends on the magnitude of the force, the displacement, and the angle between them. The angle (θ\theta) determines whether the work is positive or negative. For example, if the force and displacement are in the same direction, the work done is positive, whereas if they are in opposite directions, the work is negative. Even though work involves both force and displacement (which are vectors), its scalar nature arises because it is a product of the magnitudes of these vectors, with direction being accounted for in the angle.
Explanation:
Work is a fundamental concept in the study of energy transfer. When work is done on an object, energy is transferred to that object, resulting in a change in its kinetic or potential energy. If no displacement occurs, no work is done, even if a force is applied. For instance, if you push on a wall but it does not move, no work is done on the wall. This definition of work connects the physical concept of force with energy, making it essential in various fields like mechanics, thermodynamics, and engineering.