The product of the force and the displacement in the direction of the force.
Explanation
In physics, work is a scalar quantity that measures the energy transfer occurring when an object is moved over a distance by an external force. The scientific definition of work differs from the colloquial usage; strictly, work is done only when a force causes a displacement of the object.
Option Analysis
- The product of the force and the time for which it acts. is incorrect: The product of force and time ($F \times t$) defines Impulse. According to the impulse-momentum theorem, this quantity is equal to the change in linear momentum of the object, not work.
- The product of the force and the displacement in the direction of the force. is correct: Work is mathematically defined as the product of the component of the force in the direction of the displacement and the magnitude of this displacement. The formula is given by $W = \vec{F} \cdot \vec{d} = Fd \cos \theta$, where $\theta$ is the angle between the force vector and the displacement vector. When the force acts along the direction of motion ($\theta = 0^\circ$), work is simply the product of force and displacement ($W = F \times d$).
- The ratio of force applied to the mass of the object. is incorrect: The ratio of force applied to the mass of the object ($F/m$) defines Acceleration, in accordance with Newton's Second Law of Motion ($a = F/m$).
- The product of mass, acceleration, and time. is incorrect: The product of mass, acceleration, and time ($m \times a \times t$) simplifies to Force $\times$ Time ($F \times t$), which represents Impulse or the change in momentum, rather than work.
Key Takeaway
Work is defined as the dot product of force and displacement ($W = \vec{F} \cdot \vec{d}$). It is a scalar quantity, and its SI unit is the Joule (J).