Force and Laws of Motion

This chapter introduces Newton’s Laws of Motion, explains the concept of force, inertia, momentum, and gives a mathematical foundation to understand how and why objects move or stop moving.

🔹 Key Topics Covered

Balanced and Unbalanced Forces
First Law of Motion (Inertia)
Second Law of Motion (F = ma)
Third Law of Motion (Action = Reaction)
Concept of Momentum
Law of Conservation of Momentum
Real-life Applications

🔷 1. Force

🔸 What is Force?

A force is a push or pull on an object that may change its state of rest or motion, direction, shape, or speed.

Force has both magnitude and direction, so it is a vector quantity.
SI Unit: Newton (N)

🔸 Types of Forces

Balanced Force:
- Forces acting on an object that do not change its state of motion.
- The net force is zero.
- Example: Tug of war with equal strength teams.

Unbalanced Force:
- Forces that cause a change in the state of motion.
- Net force is non-zero.
- Example: Pushing a stationary car until it starts moving.

🔷 2. Newton’s Laws of Motion

🔸 First Law of Motion – Law of Inertia

“An object at rest remains at rest and an object in motion continues to be in motion with the same speed and direction unless acted upon by an unbalanced force.”

Explains inertia – the tendency of a body to resist change in its state.
No force = No change in motion.

🧠 Examples:

Passengers fall forward when a bus suddenly stops.
Book remains at rest on a table until pushed.

🔸 Inertia

Property of a body to resist a change in its state of rest or motion.
Greater mass = Greater inertia.

1. Which of the following has more inertia: (a) a rubber ball and a stone of the same size? (b) a bicycle and a train? (c) a five-rupees coin and a one-rupee coin?

Inertia depends on mass.

(a) The stone has more mass than the rubber ball → more inertia.
(b) The train has much more mass than the bicycle → more inertia.
(c) The five-rupees coin is heavier → more inertia.

2. In the following example, try to identify the number of times the velocity of the ball changes: “A football player kicks a football to another player of his team who kicks the football towards the goal. The goalkeeper of the opposite team collects the football and kicks it towards a player of his own team.” Also identify the agent supplying the force in each case.

Changes in velocity occur:
1. First player kicks the ball → velocity changes.
2. Second player kicks towards goal → velocity changes.
3. Goalkeeper collects and kicks again → velocity changes.

Agents applying force:
– First football player
– Second football player
– Goalkeeper

3. Explain why some of the leaves may get detached from a tree if we vigorously shake its branch.

Leaves remain at rest due to inertia. When the branch is shaken quickly, the branch moves but leaves tend to remain in their original position. Due to this difference in motion, the leaves may get detached.

This is an example of Newton’s First Law of Motion (Inertia).

4. Why do you fall in the forward direction when a moving bus brakes to a stop and fall backwards when it accelerates from rest?

– When the bus stops suddenly, the lower part of the body stops with the bus but the upper part continues moving forward due to inertia → the body falls forward.
– When the bus accelerates, the lower part moves with the bus, but the upper body tends to remain at rest → the body falls backward.

This is due to inertia of rest and motion.

🔸 Second Law of Motion

“The rate of change of momentum of an object is directly proportional to the applied unbalanced force and takes place in the direction of the force.”

📘 Formula:

$F = ma$

Where:

$F$ = Force
$m$ = Mass of the object
$a$ = Acceleration

🧠 Examples:

Kicking a football (lighter) vs. a cricket ball (heavier) → Football moves faster.

🔸 Momentum (p)

“The product of mass and velocity of an object.”

$\text{Momentum (p)} = m \times v$

Vector quantity
Unit: kg·m/s

🔸 Law of Conservation of Momentum

“Total momentum of two objects before and after collision is equal, provided no external force acts on them.”

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

Where:

$m_1, m_2$ = masses
$u_1, u_2$ = initial velocities
$v_1, v_2$ = final velocities

🔸 Third Law of Motion

“To every action, there is an equal and opposite reaction.”

Action and reaction forces act on different bodies.
Example: Walking, jumping, firing a gun, rocket launch.

🔷 Important Formulas Summary

Concept	Formula	Unit
Force	$F = ma$	N (kg·m/s²)
Momentum	$p = mv$	kg·m/s
Change in momentum	$\Delta p = mv - mu$	kg·m/s
Newton’s Second Law	$F = \frac{mv - mu}{t}$	N

🔷 Real-life Applications

Wearing seat belts (Inertia)
Paddling a bicycle (Action-Reaction)
Collisions in sports
Rockets using Newton’s Third Law

🔷 Practice-Based Understanding

📊 Example:

A 10 kg object is acted upon by a force of 20 N. What is its acceleration?

$F = ma \Rightarrow a = \frac{F}{m} = \frac{20}{10} = 2 \, \text{m/s²}$

✅ Conclusion

This chapter builds the base for understanding dynamics. It connects abstract concepts like inertia and momentum to real-world examples, helping learners form a strong foundation in physics.

Exercise

1. An object experiences a net zero external unbalanced force. Is it possible for the object to be travelling with a non-zero velocity? If yes, state the conditions that must be placed on it.

Yes, it is possible. If the object is moving with a constant velocity in a straight line, the net external force acting on it is zero. This is in accordance with Newton’s First Law. The condition is: the object must not experience any net unbalanced force, so it continues with uniform motion.

2. When a carpet is beaten with a stick, dust comes out of it. Explain.

When the carpet is beaten, the carpet comes into motion suddenly. But the dust particles remain at rest due to inertia. As a result, the dust falls out of the carpet.

3. Why is it advised to tie any luggage kept on the roof of a bus with a rope?

Due to inertia, when the bus suddenly starts or stops, the luggage may slide or fall. Tying the luggage with a rope prevents it from falling off due to sudden changes in motion.

4. A batsman hits a cricket ball which then rolls on a level ground. After covering a short distance, the ball comes to rest. The ball slows to a stop because:

Correct Option: (c) there is a force on the ball opposing the motion.
The force of friction between the ball and ground opposes the motion, causing it to slow down and stop.

5. A truck starts from rest and rolls down a hill with a constant acceleration. It travels a distance of 400 m in 20 s. Find its acceleration. Find the force acting on it if its mass is 7 tonnes.

Given: s = 400 m, u = 0, t = 20 s, mass = 7000 kg
Using: s = ut + ½ at²
400 = 0 + ½ × a × 400 ⇒ a = 400 / 200 = 2 m/s²
Force: F = ma = 7000 × 2 = 14000 N
Answer: Acceleration = 2 m/s², Force = 14000 N

6. A stone of 1 kg is thrown with a velocity of 20 m/s across the frozen surface of a lake and comes to rest after travelling a distance of 50 m. What is the force of friction between the stone and the ice?

Given: u = 20 m/s, v = 0, s = 50 m, m = 1 kg
Using: v² = u² + 2as
0 = 400 + 2a × 50 ⇒ a = -4 m/s²
Force of friction: F = ma = 1 × (-4) = -4 N
(Negative sign shows friction opposes motion)
Answer: Force of friction = 4 N

7. A 8000 kg engine pulls a train of 5 wagons, each of 2000 kg, along a horizontal track. If the engine exerts a force of 40000 N and the track offers a friction force of 5000 N, then calculate: (a) the net accelerating force (b) the acceleration of the train

Total mass = 8000 + 5 × 2000 = 18000 kg
Net force = 40000 − 5000 = 35000 N
Acceleration = F / m = 35000 / 18000 ≈ 1.94 m/s²

Answer:
(a) Net accelerating force = 35000 N
(b) Acceleration = 1.94 m/s²

8. An automobile vehicle has a mass of 1500 kg. What must be the force between the vehicle and road if the vehicle is to be stopped with a negative acceleration of 1.7 m/s²?

F = ma = 1500 × (–1.7) = –2550 N
Answer: 2550 N (opposing direction indicates retardation)

9. What is the momentum of an object of mass m, moving with velocity v?

Answer: Option (d) mv

10. Using a horizontal force of 200 N, we intend to move a wooden cabinet across a floor at constant velocity. What is the friction force exerted on the cabinet?

At constant velocity, net force = 0 ⇒ friction = applied force
Answer: 200 N

11. A student says the two equal and opposite forces cancel each other when we push a truck, so the truck does not move. Comment on this logic.

The forces act on two different bodies: you exert force on the truck, and the truck exerts force on you. These do not cancel each other. If friction is high or the truck is heavy, it won’t move despite your force.

12. A hockey ball of mass 200 g moving at 10 m/s is struck by a stick to return with a velocity of 5 m/s. What is the magnitude of change in momentum?

Mass = 0.2 kg
Initial momentum = 0.2 × 10 = 2 kg·m/s
Final momentum = 0.2 × (–5) = –1 kg·m/s
Change = Final – Initial = –1 – 2 = –3 kg·m/s
Magnitude = 3 kg·m/s

13. A bullet of mass 10 g travelling at 150 m/s hits a wooden block and stops in 0.03 s. Find the distance penetrated and force exerted.

m = 0.01 kg, u = 150 m/s, v = 0, t = 0.03 s
a = (0 – 150)/0.03 = –5000 m/s²
s = ut + ½at² = 150×0.03 + 0.5×(–5000)×(0.03)² = 4.5 – 2.25 = 2.25 m
F = ma = 0.01 × 5000 = 50 N
Answer: Penetration = 2.25 m, Force = 50 N

14. A 1 kg object moving at 10 m/s collides with and sticks to a 5 kg block at rest. Find total momentum and velocity after collision.

Initial momentum = 1 × 10 + 5 × 0 = 10 kg·m/s
Total mass = 1 + 5 = 6 kg
v = p/m = 10/6 = 1.67 m/s
Answer: Final velocity = 1.67 m/s

15. An object of mass 100 kg accelerates from 5 m/s to 8 m/s in 6 s. Find initial and final momentum and the force exerted.

Initial p = 100 × 5 = 500 kg·m/s
Final p = 100 × 8 = 800 kg·m/s
Change = 300 kg·m/s
Force = Δp / t = 300 / 6 = 50 N
Answer: Initial = 500, Final = 800, Force = 50 N

16. Three students argue about why an insect dies when it hits a speeding car’s windshield. Who is right?

All are partially correct:
– The insect has larger change in velocity → large Δp
– The car has more mass but less velocity change
– According to Newton’s 3rd Law, both experience equal and opposite force.
The insect dies because it cannot withstand the force, unlike the car.

17. How much momentum will a 10 kg dumb-bell transfer if it falls from 80 cm? Take g = 10 m/s².

h = 0.8 m, m = 10 kg
v = √(2gh) = √(2×10×0.8) = √16 = 4 m/s
p = mv = 10 × 4 = 40 kg·m/s
Answer: Momentum = 40 kg·m/s

Additional

A1. The following is the distance-time table of an object in motion:

Time (s):     0   1   2    3    4     5     6     7  
Distance (m): 0   1   8   27   64   125   216   343

(a) What conclusion can you draw about the acceleration?
(b) What do you infer about the forces acting on the object?

(a) The distance is increasing rapidly. The object covers more distance in each second, indicating non-uniform acceleration which is increasing.

(b) Since the object is accelerating, there must be a net unbalanced force acting on it in the direction of motion.

A2. Two persons push a motorcar (mass = 1200 kg) at uniform velocity. Three persons produce an acceleration of 0.2 m/s². What force does each person apply?

Total force (F) = ma = 1200 × 0.2 = 240 N
This force is produced by 3 persons.
Force by each person = 240 / 3 = 80 N
Answer: Each person applies 80 N of force.

A3. A hammer of mass 500 g moving at 50 m/s strikes a nail and is stopped in 0.01 s. What is the force of the nail on the hammer?

m = 0.5 kg, u = 50 m/s, v = 0, t = 0.01 s
a = (v – u) / t = (0 – 50) / 0.01 = –5000 m/s²
F = ma = 0.5 × (–5000) = –2500 N
Answer: 2500 N (opposite direction indicates the nail stops the hammer)

A4. A motorcar of mass 1200 kg is moving with uniform velocity of 90 km/h. It slows to 18 km/h in 4 s. Calculate: (a) acceleration, (b) change in momentum, (c) force required.

Convert velocities: u = 90 km/h = 25 m/s, v = 18 km/h = 5 m/s
t = 4 s, m = 1200 kg

(a) Acceleration: a = (v – u)/t = (5 – 25)/4 = –5 m/s²

(b) Change in momentum: Δp = m(v – u) = 1200 × (5 – 25) = –24000 kg·m/s

(c) Force: F = ma = 1200 × (–5) = –6000 N
Answer: Acceleration = –5 m/s², Change in momentum = –24000 kg·m/s, Force = 6000 N

🔷 Chapter Overview

🔹 Key Topics Covered