Negative work occurs when the force applied and the displacement are in opposite directions. This means the force is working against the motion, decreasing the object's kinetic energy.
Understanding Work
Work, in physics, is the energy transferred to or from an object by a force causing a displacement. Work can be positive, negative, or zero. The formula for work is typically expressed as:
W = F d cos(θ)
Where:
- W is the work done
- F is the magnitude of the force
- d is the magnitude of the displacement
- θ is the angle between the force and displacement vectors.
Defining Negative Work
As stated in the provided reference, negative work happens "when the displacement is in the opposite orientation of the force delivered." In simpler terms, if you're pushing against the direction something is moving, you're doing negative work on it. The angle θ in the work equation would be greater than 90 degrees, resulting in a negative cosine value and therefore negative work.
Examples of Negative Work
Here are some examples to illustrate the concept:
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Gravity on a rocket moving upwards: According to the reference, "The gravity on some kind of rocket moving vertically upwards was worked on." Gravity is pulling downwards, while the rocket is moving upwards. This is a classic example of negative work. Gravity is reducing the rocket's kinetic energy, making it slow down (if the rocket's engine doesn't provide enough thrust).
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Friction: Friction always opposes motion. When you slide a box across the floor, friction does negative work, slowing the box down.
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Applying Brakes: When you apply the brakes in a car, the brake pads exert a force opposing the car's motion. This negative work reduces the car's kinetic energy and slows it down.
When is Work Zero?
The provided reference also mentions zero work: "Zero work: Whenever force and displacement, are perpendicular to one another, or even when either force or displacement is zero."
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Perpendicular Force and Displacement: Imagine carrying a book horizontally while walking. The force you exert (upwards) is perpendicular to the displacement (horizontal). You are doing no work on the book in the physics sense, even though it may feel like work!
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No Displacement: If you push against a stationary wall, you're exerting a force, but there's no displacement. Therefore, no work is done.
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No Force: If there is no force applied to an object, then no work is done.
Table Summarizing Work
| Type of Work | Force and Displacement Relationship | Angle (θ) | Resulting Change in Kinetic Energy | Example |
|---|---|---|---|---|
| Positive | Force and displacement in same direction | 0° < θ < 90° | Increase | Pushing a box across the floor |
| Negative | Force and displacement in opposite direction | 90° < θ ≤ 180° | Decrease | Gravity acting on a rising object |
| Zero | Force and displacement perpendicular or either force or displacement is zero | θ = 90° or F=0 or d=0 | No change | Carrying a book horizontally, pushing a wall |
