8.1 Work Explained
Key Concepts
1. Definition of Work
Work is defined as the product of the force applied to an object and the distance the object moves in the direction of the force. Mathematically, it is expressed as W = Fd, where W is work, F is force, and d is distance.
2. Units of Work
The SI unit of work is the joule (J), which is equivalent to one newton-meter (N·m). One joule of work is done when a force of one newton is applied over a distance of one meter.
3. Conditions for Work to be Done
For work to be done, two conditions must be met: a force must be applied to an object, and the object must move in the direction of the applied force.
4. Work and Energy
Work is closely related to energy. When work is done on an object, energy is transferred to that object. The amount of work done is equal to the change in energy of the object.
5. Negative Work
Negative work occurs when the force applied is opposite to the direction of motion. This results in a decrease in the object's energy.
Detailed Explanation
Definition of Work
Work is a measure of the energy transferred when a force acts on an object and causes it to move. For example, if you push a box with a force of 10 N over a distance of 5 meters, the work done is W = 10 N × 5 m = 50 J.
Units of Work
The joule (J) is the standard unit of work. It is named after the English physicist James Prescott Joule. For instance, lifting a book from the floor to a table involves doing work, and the amount of work done can be measured in joules.
Conditions for Work to be Done
For work to be considered done, the force must cause the object to move. If you push against a wall but the wall does not move, no work is done because there is no displacement. Similarly, if you carry a heavy bag while walking horizontally, the force of gravity does no work on the bag because the vertical displacement is zero.
Work and Energy
Work and energy are interchangeable. When you do work on an object, you transfer energy to it. For example, when you lift a weight, you do work against gravity, and the potential energy of the weight increases. Conversely, when a ball falls, gravity does work on the ball, converting potential energy into kinetic energy.
Negative Work
Negative work happens when the force opposes the motion. For instance, when you slow down a moving car by applying the brakes, the friction force does negative work, reducing the car's kinetic energy. Similarly, when a ball is thrown upwards, gravity does negative work on the ball, slowing it down until it reaches its maximum height.
Examples and Analogies
Example: Pushing a Cart
When you push a shopping cart with a force of 20 N over a distance of 10 meters, the work done is W = 20 N × 10 m = 200 J. This means you have transferred 200 joules of energy to the cart.
Analogy: Pushing a Heavy Object
Think of work as pushing a heavy object across a room. The harder you push (force) and the farther you push it (distance), the more work you do. Just as you exert effort to move the object, you are transferring energy to it.
Example: Lifting a Book
When you lift a book from the floor to a table, you do work against gravity. If the book weighs 2 N and the table is 1 meter high, the work done is W = 2 N × 1 m = 2 J. This means you have increased the book's potential energy by 2 joules.
Analogy: Lifting a Weight
Consider lifting a weight in a gym. The more weight you lift (force) and the higher you lift it (distance), the more work you do. This work increases the weight's potential energy.
Example: Slowing Down a Car
When you apply the brakes to slow down a car, the friction force does negative work. If the car is moving at 10 m/s and you apply a braking force of 500 N over a distance of 20 meters, the work done is W = -500 N × 20 m = -10,000 J. This negative work reduces the car's kinetic energy.
Analogy: Slowing Down a Skateboard
Think of slowing down a skateboard by dragging your foot. The force you apply (friction) opposes the motion, doing negative work and reducing the skateboard's speed. This is similar to how brakes work in a car.