Work Done & Energy Transfer

• The principle of Energy Conservation dictates that energy cannot be created or destroyed, only transferred. Work done is the mechanism for this transfer.

• When work is done on an object, energy is transferred into one of its stores. For example, lifting an object vertically transfers energy into its gravitational potential energy (GPE) store.

• The relationship is numerically direct: $1 Joule$ of work done results in exactly $1 Joule$ of energy transferred. This allows for the calculation of energy changes using mechanical variables.

• The mathematical foundation is expressed by the formula: $W = F \times s$ where $W$ is work done ($J$), $F$ is force ($N$), and $s$ is distance ($m$).

Calculating Work Done

• Step 1: Identify the Force: Determine the specific force doing the work (e.g., engine force, weight, or friction). Ensure the force is in Newtons ($N$).
• Step 2: Determine Displacement: Measure the distance moved specifically in the direction of the force. If an object moves horizontally while being pulled vertically, the vertical force does no work on the horizontal motion.
• Step 3: Apply the Formula: Multiply the force by the distance ($W = F \times s$).

Calculating Energy Changes

• To find the energy transferred when lifting an object, use the weight of the object as the force ($F = m \times g$) and the height as the distance ($s = h$).
• This results in the derived formula for gravitational potential energy: $E_p = m \times g \times h$.

• Friction is a resistive force that acts in the opposite direction to an object's motion. When an object moves against friction, work is done to overcome this resistance.

• This work done against friction does not disappear; it is transferred into the thermal energy store of the object and its surroundings.

• On a microscopic level, friction is caused by surface imperfections rubbing together. The mechanical work required to move these surfaces results in increased atomic vibrations, which we perceive as a rise in temperature.

• Air resistance (drag) is a form of fluid friction. Objects moving through the air do work against air particles, transferring kinetic energy into the thermal store of the air.

• Unit Consistency: Always check that distance is in metres ($m$) and force is in Newtons ($N$). If a mass is given in $kg$, you must multiply by gravitational field strength ($g \approx 9.8 N/kg$) to find the force (weight) before calculating work.

• The 'Zero Work' Trap: Examiners often describe scenarios where a large force is applied but no movement occurs (e.g., pushing a wall). In these cases, work done is always $0 J$.

• Interchangeable Units: Remember that $J$ and $N m$ are identical. If a question asks for work in $N m$, do not feel the need to convert it to $J$ unless specified.

• Sanity Check: If an object is slowing down, the work done by the driving force is likely zero, and the work is being done by friction/braking forces instead.