# Work and Energy ## What is Work? Work, in physics, isn't just any activity. It's specifically defined as the energy transferred to or from an object via the application of a force along a displacement. Think of it this way: work is done only when a force causes an object to move *in the direction of the force*. Pushing against a wall doesn't do any work, because the wall doesn't move. However, pushing a box across the floor *does* do work. Here are some everyday examples of work being done: * Lifting a weight * Pushing a shopping cart * Pulling a sled * Climbing stairs Imagine lifting a 10kg weight 1 meter off the ground. You're applying a force (to counteract gravity) over a distance, thus doing work. ## Calculating Work Done The amount of work done (W) is calculated using the following formula: $$W = F \times d$$ Where: * **W** represents work done, measured in Joules (J) * **F** represents the force applied, measured in Newtons (N) * **d** represents the distance moved in the direction of the force, measured in meters (m) Remember that the distance 'd' is only the distance moved *in the direction of the force*. If you lift a box vertically, the horizontal movement doesn't contribute to the work done. Let's say you push a box with a force of 20 N across a floor for a distance of 5 m. The work done is: W = 20 N × 5 m = 100 J A common mistake is to forget that the force and distance must be in the same direction. Only the component of the force in the direction of motion contributes to the work done. ## Work and Energy: The Connection Work and energy are intimately related. The work done on an object is equal to the change in its energy. This is a fundamental principle of physics. Energy is the capacity to do work. You need energy to do work, but having energy doesn't automatically mean you're doing work. There are different forms of energy: * **Potential Energy:** Energy stored due to an object's position or configuration (e.g., gravitational potential energy, elastic potential energy). * **Kinetic Energy:** Energy of motion. * **Elastic Energy:** Energy stored in a deformed object (like a stretched spring). Understanding the relationship between work and energy helps solve many physics problems. If you know the work done, you know the change in energy. ## Rearranging the Work Equation The work equation ($W = F \times d$) can be rearranged to solve for force or distance: * To find force: $F = \frac{W}{d}$ * To find distance: $d = \frac{W}{F}$ Use the triangle method to remember how to rearrange the equation. Cover the variable you want to find, and the remaining variables show you the operation (multiplication or division). ## Key Takeaways * Work is done when a force causes an object to move in the direction of the force. * Work is calculated as: $W = F \times d$ * Work done is equal to the change in energy. * The units of work are Joules (J). This concludes the study notes on work. Remember to practice solving problems using the formula and understanding the relationship between work and energy.