1. What is Force?
- Force is a push or pull that changes or tends to change the state of motion of an object.
- SI Unit: Newton (N)
- Formula:Force (F)=Mass (m)×Acceleration (a)(Derived from Newton’s Second Law)
2. Types of Forces
- Contact Forces (require physical contact):
- Frictional Force
- Tension Force
- Normal Force
- Non-Contact Forces (act at a distance):
- Gravitational Force
- Magnetic Force
- Electrostatic Force
3. Newton’s Three Laws of Motion
(a) Newton’s First Law (Law of Inertia)
- Statement: An object remains in its state of rest or uniform motion unless acted upon by an external unbalanced force.
- Example: A book on a table stays at rest until someone pushes it.
- Inertia: The tendency of an object to resist changes in its motion.
- Mass is a measure of inertia (heavier objects resist change more).
(b) Newton’s Second Law (Force-Acceleration Relationship)
- Statement: The rate of change of momentum of an object is directly proportional to the applied force and takes place in the direction of the force.
- Formula:F=m×a
- Momentum (p) = Mass (m) × Velocity (v)
- If force increases, acceleration increases (if mass is constant).
- Example: Kicking a football (greater force → greater acceleration).
(c) Newton’s Third Law (Action-Reaction Law)
- Statement: For every action, there is an equal and opposite reaction.
- Example:
- Walking (you push the ground backward, the ground pushes you forward).
- Rocket propulsion (exhaust gases push downward, rocket moves upward).
4. Important Formulas
| Concept | Formula |
|---|---|
| Force | F=m×aF=m×a |
| Momentum | p=m×vp=m×v |
| Impulse (Change in Momentum) | J=F×ΔtJ=F×Δt |
| Acceleration | a=Fma=mF |
5. Practical Applications
- Seatbelts in Cars: Prevent injury due to inertia (First Law).
- Cricket Ball vs Tennis Ball: A cricket ball (more mass) requires more force to accelerate (Second Law).
- Recoil of a Gun: When a bullet is fired forward, the gun moves backward (Third Law).
6. Sample Questions (RRB Group D Style)
- What is the SI unit of force?
- Answer: Newton (N).
- If a 5 kg object accelerates at 2 m/s², what is the force applied?
- Solution: F=m×a=5×2=10 NF=m×a=5×2=10N.
- Which law explains why a passenger leans forward when a car suddenly stops?
- Answer: Newton’s First Law (Inertia).
Numerical Problems on Force and Laws of Motion
1. Problems Based on Newton’s Second Law (F = ma)
Q1: A car of mass 1000 kg accelerates at 2 m/s². Calculate the force applied by the engine.
Solution:
Given:
- Mass (m) = 1000 kg
- Acceleration (a) = 2 m/s²
Using Newton’s Second Law:F=m×a
F=1000×2=2000 N (Force unit is Newton)
Answer: 2000 N
Q2: A force of 500 N acts on a body of mass 25 kg. Find its acceleration.
Solution:
Given:
- Force (F) = 500 N
- Mass (m) = 25 kg
Using F = ma:
a=F/m=500/25=20 m/s²
Answer: 20 m/s²
2. Problems Based on Momentum (p = mv)
Q3: A bullet of mass 0.02 kg is fired at 400 m/s. Calculate its momentum.
Solution:
Given:
- Mass (m) = 0.02 kg
- Velocity (v) = 400 m/s
Using Momentum Formula:p=m×v, p=0.02×400=8 kg m/s
Answer: 8 kg m/s
Q4: A cricket ball of mass 0.15 kg is moving with a momentum of 3 kg m/s. Find its velocity.
Solution:
Given:
- Momentum (p) = 3 kg m/s
- Mass (m) = 0.15 kg
Using p = mv:v=p/m=3/0.15=20 m/s
Answer: 20 m/s
3. Problems Based on Impulse (Change in Momentum)
Q5: A force of 200 N acts on a body for 5 seconds. Calculate the impulse.
Solution:
Given:
- Force (F) = 200 N
- Time (Δt) = 5 s
Using Impulse Formula (J = F × Δt):J=200×5=1000 N s
Answer: 1000 Ns
Q6: A ball of mass 0.5 kg hits a wall at 10 m/s and rebounds at 8 m/s. Find the change in momentum.
Solution:
Given:
- Mass (m) = 0.5 kg
- Initial velocity (u) = +10 m/s (towards the wall)
- Final velocity (v) = -8 m/s (rebound, opposite direction)
Change in momentum (Δp) = m(v – u)
Δp=0.5×(−8−10)
Δp=0.5×(−18)=−9 kg m/s
(The negative sign indicates a change in direction.)
Answer: 9 kg m/s (magnitude)
4. Problems Based on Newton’s Third Law (Action-Reaction)
Q7: A man pushes a wall with a force of 50 N. What is the reaction force exerted by the wall?
Solution:
- According to Newton’s Third Law, the wall exerts an equal and opposite force of 50 N back on the man.
Answer: 50 N (in the opposite direction)
5. Mixed Problems (Combining Concepts)
Q8: A 1200 kg car accelerates from 0 to 20 m/s in 5 seconds. Calculate:
(i) Acceleration
(ii) Force applied
(iii) Change in momentum
Solution:
Given:
- Mass (m) = 1200 kg
- Initial velocity (u) = 0 m/s
- Final velocity (v) = 20 m/s
- Time (Δt) = 5 s
(i) Acceleration (a):a=v−ut=20/5=4 m/s²
(ii) Force (F):F=m×a=1200×4=4800 N
(iii) Change in Momentum (Δp):Δp=m(v−u)=1200×(20−0)=24000 kg m/s
Answers:
(i) 4 m/s²
(ii) 4800 N
(iii) 24000 kg m/s
MCQs on Force and Laws of Motion
1. What is the SI unit of force?
a) Joule
b) Newton
c) Watt
d) Pascal
✅ Answer: (b) Newton
- Force is measured in Newtons (N).
2. Newton’s First Law of Motion is also called:
a) Law of Momentum
b) Law of Inertia
c) Law of Action-Reaction
d) Law of Acceleration
✅ Answer: (b) Law of Inertia
- It states that an object resists changes in its state of motion.
3. If a net force of 50 N acts on a 10 kg object, what is its acceleration?
a) 5 m/s²
b) 500 m/s²
c) 0.2 m/s²
d) 2 m/s²
✅ Answer: (a) 5 m/s²
- Using F = ma → a=F/m=50/10=5 m/s²
4. Which of the following is an example of Newton’s Third Law?
a) A ball rolling on the ground stops due to friction.
b) A rocket moves upward when gases are expelled downward.
c) A heavy object requires more force to accelerate.
d) A book kept on a table remains at rest.
✅ Answer: (b) A rocket moves upward when gases are expelled downward.
- Action (gases pushed down) → Reaction (rocket moves up).
5. The momentum of a 5 kg object moving at 4 m/s is:
a) 20 kg m/s
b) 1.25 kg m/s
c) 9 kg m/s
d) 0.8 kg m/s
✅ Answer: (a) 20 kg m/s
- Momentum (p) = m × v = 5 × 4 = 20 kg m/s.
6. Which law explains why a passenger leans forward when a car suddenly brakes?
a) Newton’s First Law
b) Newton’s Second Law
c) Newton’s Third Law
d) Law of Gravitation
✅ Answer: (a) Newton’s First Law (Inertia)
- The body tends to stay in motion even when the car stops.
7. A force of 100 N acts on a body for 2 seconds. What is the impulse imparted?
a) 50 Ns
b) 200 Ns
c) 100 Ns
d) 0.02 Ns
✅ Answer: (b) 200 Ns
- Impulse (J) = F × Δt = 100 × 2 = 200 Ns.
8. If the mass of an object is doubled while keeping the force constant, its acceleration will:
a) Double
b) Remain the same
c) Halve
d) Become zero
✅ Answer: (c) Halve
- From F = ma, if m increases, a decreases proportionally.
9. What is the force required to accelerate a 500 kg car at 3 m/s²?
a) 1500 N
b) 166.67 N
c) 0.006 N
d) 503 N
✅ Answer: (a) 1500 N
- F = m × a = 500 × 3 = 1500 N.
10. A bullet of mass 0.01 kg is fired at 300 m/s. What is its momentum?
a) 3 kg m/s
b) 30 kg m/s
c) 0.03 kg m/s
d) 3000 kg m/s
✅ Answer: (a) 3 kg m/s
- Momentum (p) = m × v = 0.01 × 300 = 3 kg m/s.
