Laws of Motion – KCET Physics Study Notes
Objective:
Master Newton’s three laws, their mathematical expressions, and how to apply them in common KCET problems (free‑body diagrams, sliding blocks, inclines, friction, projectile motion).
1. Simple Explanation
| Concept | What it Says | Why it Matters |
|---|---|---|
| Inertia | A body at rest stays at rest; a body in motion stays in uniform straight‑line motion. | Explains why we feel a “push” when a car brakes. |
| Force = Mass × Acceleration | Any change in motion (speed or direction) requires a net force. | Quantifies how big a push is needed to accelerate a given mass. |
| Action–Reaction | For every action, there is an equal and opposite reaction. | Helps analyze forces in systems (e.g., a rocket, a swimmer). |
2. Newton’s Three Laws (in Detail)
2.1 Newton’s First Law (Law of Inertia)
- Statement:
A particle remains at rest or moves at a constant velocity unless acted upon by a net external force. - Implication:
Net external force ( \Sigma \mathbf{F} = 0 ) → ( \mathbf{a} = 0 ). - Common Misconception:
Inertia is not a force; it’s a property of mass.
2.2 Newton’s Second Law
- Vector form:
[ \boxed{\mathbf{F}_{\text{net}} = m \mathbf{a}} ] - Components:
( F_x = m a_x ), ( F_y = m a_y ) … etc. - Units:
Force in N, mass in kg, acceleration in m s⁻². - Key Points:
Net force is the vector sum of all forces.
Direction of acceleration is the direction of ( \mathbf{F}_{\text{net}} ).
2.3 Newton’s Third Law
- Statement:
For every force ( \mathbf{F}{12} ) exerted by body 1 on body 2, there is an equal and opposite force ( \mathbf{F}{21} ) exerted by body 2 on body 1. - Mathematically:
[ \mathbf{F}{12} = - \mathbf{F}{21} ] - Applications:
Rocket thrust, swimmer’s propulsion, a person pushing off a wall.
3. Key Concepts & Definitions
| Concept | Symbol | Typical Value / Note |
|---|---|---|
| Mass | (m) | Invariant; measured in kg. |
| Weight | (W) | ( W = m g ). |
| Normal Force | (N) | Perpendicular to contact surface. |
| Friction | (F_f) | ( F_f = \mu N ) (kinetic) or ( \le \mu_s N ) (static). |
| Coefficient of Friction | ( \mu ) | Dimensionless. |
| Gravitational Acceleration | ( g ) | ≈ 9.81 m s⁻² on Earth. |
| Incline Angle | ( \theta ) | Angle of slope with horizontal. |
4. Free‑Body Diagram (FBD) – A Quick Guide
- Identify the object under study.
- List all forces acting on it (weight, normal, friction, tension, applied push).
- Draw vectors for each force, pointing in the correct directions.
- Resolve forces into components if needed.
- Apply Newton’s 2nd Law along each axis:
[ \Sigma F_x = m a_x,\qquad \Sigma F_y = m a_y. ]
5. Worked Example (KCET‑style)
Problem:
A 5 kg block slides down a 30° incline. The coefficient of kinetic friction between the block and the surface is 0.20. Find the block’s acceleration.
Step‑by‑Step Solution
| Step | Calculation | Result |
|---|---|---|
| 1. Resolve weight → parallel & perpendicular | ( W = m g = 5 \times 9.81 = 49.05;\text{N} ) | |
| 2. Parallel component | ( W_{\parallel} = W \sin \theta = 49.05 \sin 30^\circ = 24.525;\text{N} ) | |
| 3. Perpendicular |