Zero
Explanation
Power is defined as the rate at which work is done or energy is transferred. In vector notation, power ($P$) is expressed as the dot product of the force vector ($\vec{F}$) and the velocity vector ($\vec{v}$).
Detailed Analysis
The mathematical expression for power is given by:
$$P = \vec{F} \cdot \vec{v} = F v \cos \theta$$
Where:
- $F$ is the magnitude of the applied force.
- $v$ is the magnitude of the velocity.
- $\theta$ is the angle between the direction of the force and the direction of motion (velocity).
The object moves in a direction perpendicular to the line of action of the applied force. Therefore, the angle $\theta$ is $90^\circ$.
Substituting this value into the equation:
$$P = F v \cos 90^\circ$$
Since $\cos 90^\circ = 0$, the power becomes:
$$P = 0$$
Consequently, no work is done by the force, and the power expended is zero.
Key Takeaway: If a force acts perpendicular to the direction of displacement (e.g., centripetal force in circular motion), the work done by that force is zero, and the power expended is zero.