Work
Work happens when a force causes an object to move. It’s calculated using:
\[ W = F \cdot d \cdot \cos\theta \]
Where:
- \( F \) = Force applied
- \( d \) = Displacement
- \( \theta \) = Angle between force and displacement
When is work not done?
- 🚫 No displacement: Like pushing a wall that doesn’t move.
- 🚫 No force: A block sliding freely on a smooth table (no friction).
- 🚫 Force and displacement are perpendicular: Gravity does no work on a horizontally moving object.
Work can be positive or negative! If \( \theta \) is between 90°–180°, work is negative (e.g., friction opposing motion).
Kinetic Energy
Kinetic energy (\( K \)) is the energy an object has due to its motion:
\[ K = \frac{1}{2}mv^2 \]
Examples:
- A bullet (50g at 200 m/s) has 1000 J of kinetic energy.
- If it loses 90% energy, its speed drops to ~63.2 m/s (not 90% slower!).
Work Done by a Variable Force
For changing forces, work is the area under the force-displacement graph. Use integration:
\[ W = \int_{x_i}^{x_f} F(x) \, dx \]
Small displacements (\( \Delta x \)) approximate constant force: \( \Delta W = F(x) \cdot \Delta x \).
Important NEET Concepts
- ⭐ Work conditions: When is work zero? (Displacement=0, force=0, or force⊥displacement)
- ⭐ Work-Energy Theorem: Negative work (e.g., friction) removes kinetic energy.
- ⭐ Kinetic Energy calculations: Use \( K = \frac{1}{2}mv^2 \) for problems like bullet speed changes.
- ⭐ Newton’s Third Law & Work: Equal forces don’t mean equal work (e.g., cycle vs. road).
Example Problem (Solved!)
A cyclist skids 10 m. Road applies 200 N backward force. What’s the work done by the road?
Solution:
\[ W = 200 \times 10 \times \cos(180^\circ) = -2000\, \text{J} \]
Negative work = energy lost by the cycle. Road does no work because it doesn’t move!
