What is the mathematical relationship between force and work?
The mathematical relationship between force and work is that work is equal to the force multiplied by the distance over which the force is applied. Mathematically, this is expressed as W = F × d.
The mathematical relationship between force and work is given by the equation:
Work = Force x Distance x cos(theta)
where:
- Work is the energy transferred or done on an object (measured in joules, J)
- Force is the applied force on the object (measured in newtons, N)
- Distance is the displacement of the object in the direction of the applied force (measured in meters, m)
- theta is the angle between the force vector and the displacement vector (measured in degrees or radians)
The cosine of the angle theta is included in the equation to account for the fact that only the component of the force that is parallel to the displacement vector contributes to the work done.
It is important to note that work is a scalar quantity, meaning it does not have a direction, while force and displacement are vector quantities, which have both magnitude and direction.