A retarding force applied to a moving vehicle to stop it.
Explanation
In physics, work is defined as the scalar product of force and displacement. Mathematically, it is expressed as:
W = Fs cos θ
Where F is the magnitude of the force, s is the displacement, and θ is the angle between the force vector and the displacement vector. The nature of work depends on this angle:
- Positive Work: When the force aids motion (0° ≤ θ < 90°).
- Zero Work: When the force is perpendicular to motion (θ = 90°).
- Negative Work: When the force opposes motion (90° < θ ≤ 180°).
Scenario Analysis:
- A baby pulling a toy car parallel to the ground. A baby pulling a toy car parallel to the ground: The force is applied in the direction of displacement (θ = 0°). Since cos 0° = 1, the work done is positive.
- An object falling freely under gravity. An object falling freely under gravity: The gravitational force acts downwards, and the displacement is also downwards. The angle between force and displacement is 0°. Therefore, the work done by gravity is positive.
- A retarding force applied to a moving vehicle to stop it. A retarding force applied to a moving vehicle: A retarding force (such as friction or brakes) acts opposite to the direction of the vehicle's motion. The angle between the force and displacement is 180°. Since cos 180° = -1, the work done is negative.
- A cyclist pedaling to increase speed on a level road. A cyclist pedaling to increase speed: The force applied by the cyclist is in the direction of motion to overcome resistance and accelerate. The angle is 0°, resulting in positive work.
Key Takeaway:
Work done is considered negative when the force acts in the opposite direction to the displacement, effectively taking energy away from the system (e.g., friction or braking).