Unit 4.1 – Work Done

1. The magnitude of the force applied.
2. The displacement caused in the direction of the force.

• $𝐹$ = Force applied (in Newtons, N)
• $𝑠$ = Displacement (in meters, m)
• $𝜃$ = Angle between the force and displacement

1. When $𝜃=0^{\circ }$: If the force and displacement are in the same direction, $\cos 0^{\circ }=1$.
   $$𝑊=𝐹\cdot 𝑠$$
   Example: Pushing a box along a straight path.
2. When $𝜃={90}^{\circ }$: If the force is perpendicular to the displacement, $\cos {90}^{\circ }=0$.
   $$𝑊=0$$
   Example: A waiter carrying a tray horizontally does no work on the tray because the force is vertical (upward).
3. When $𝜃={180}^{\circ }$: If the force and displacement are in opposite directions, $\cos {180}^{\circ }=-1$.
   $$𝑊=-𝐹\cdot 𝑠$$
   Example: Applying brakes to stop a moving car.

1. Lifting a book from the ground involves work as the force (weight of the book) moves it upward.
2. Kicking a football causes it to move, which is also an example of work.

Quick Review, Exam Tips, Tricks & Traps

1. Work is only done if there is displacement in the direction of the force.
2. Work can be positive, negative, or zero, depending on the angle ($𝜃$) between force and displacement.

1. Always check the angle ($𝜃$) between force and displacement. Misinterpreting this leads to wrong answers.
2. Remember that no displacement = no work, even if a large force is applied. For example, pushing a wall doesn’t do work unless it moves.

1. Students often forget to include the cosine term ($\cos 𝜃$) in calculations. Always use the full formula unless $𝜃=0^{\circ }$.
2. Confusion between positive and negative work: Positive work occurs when force aids motion; negative work opposes motion.

1. Use approximations for angles:
   • $\cos 0^{\circ }=1$, $\cos {90}^{\circ }=0$, $\cos {180}^{\circ }=-1$.
2. In MCQs, eliminate options where work is claimed to happen without displacement.