Chapter 8: Force & Motion
1. What is Force?
In our daily life, we see that to move a stationary object (like a football), we need to kick it. To stop a moving car, we apply brakes.
Definition: A force is essentially a push, pull, or hit applied on an object.
1. Can change the state of motion (Rest → Motion, or Motion → Rest).
2. Can change the speed (accelerate or decelerate).
3. Can change the direction of motion.
4. Can change the shape & size (e.g., stretching a spring).
2. Balanced vs. Unbalanced Forces
Imagine a wooden block on a table with strings tied to opposite sides.
A. Balanced Forces
- If Force X = Force Y, the block does NOT move.
- The net force is zero.
- Does not change the state of rest or motion.
B. Unbalanced Forces
- If Force X > Force Y, the block moves left.
- If Force Y > Force X, the block moves right.
- Result: Motion occurs in the direction of the greater force.
- Unbalanced forces are required to accelerate an object.
C. Friction Force
When you push a box and it doesn’t move, it’s because Friction is balancing your push. Friction always acts opposite to the direction of motion.
3. First Law of Motion
Before Newton, Galileo Galilei studied motion using inclined planes and marbles.
Galileo deduced: Objects move with constant speed if no force acts on them.
Newton’s Statement:
“An object remains in a state of rest or of uniform motion in a straight line unless compelled to change that state by an applied unbalanced force.”
Also known as the Law of Inertia.
4. Inertia and Mass
Inertia: The natural tendency of an object to resist a change in its state of motion or rest.
• Heavier object (Train) = More Inertia (Hard to move/stop).
• Lighter object (Cart) = Less Inertia (Easy to move/stop).
Real Life Examples (The “Why?” questions)
Q1: Why do we fall forward when a bus brakes suddenly?
- Explanation: Our body is moving with the bus. When brakes are applied, the bus (and our feet touching the floor) stops.
- But, our upper body continues to move forward due to Inertia of Motion.
Q2: Why do we fall backward when a bus starts suddenly?
- Explanation: Our body is at rest. The bus moves forward suddenly, taking our feet with it.
- The upper body tries to stay at rest due to Inertia of Rest, so we fall back.
Q3: Why does dust fly off a carpet when beaten?
- The carpet moves suddenly due to the stick. The dust particles try to remain at rest (Inertia) and thus separate from the carpet.
5. Second Law of Motion
This law connects Force with Momentum.
Momentum (p)
Momentum is the “power” of motion possessed by an object.
- m = mass (kg)
- v = velocity (m/s)
- SI Unit: kg m/s
- It is a Vector quantity (has direction).
The Law Statement:
“The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of force.”
Mathematical Derivation (Important!)
Let an object of mass m change velocity from u (initial) to v (final) in time t.
Initial Momentum ($p_1$) = $mu$
Final Momentum ($p_2$) = $mv$
Change in momentum = $p_2 – p_1 = mv – mu = m(v – u)$
Rate of change = $\frac{m(v – u)}{t}$
According to Second Law:
$F \propto \frac{m(v – u)}{t}$
We know acceleration $a = \frac{(v – u)}{t}$, so:
$F \propto ma$
$F = kma$
(In SI units, k = 1)
F = m a
Applications: Catching a Cricket Ball
Why does a fielder pull his hands back?
- By pulling back, he increases the time (t) to stop the ball.
- Since $F \propto \frac{(Change\ in\ p)}{t}$, increasing t decreases F.
- Less force = Less hurt on hands!
6. Third Law of Motion
“To every action, there is an equal and opposite reaction.”
- Action and Reaction act on TWO DIFFERENT BODIES.
- They act simultaneously.
- They are equal in magnitude but opposite in direction.
Common Examples
You push ground backward (Action). Ground pushes you forward (Reaction).
Gun exerts force on bullet (forward). Bullet exerts force on gun (backward/recoil).
7. Conservation of Momentum
(Often connected with 3rd Law)
In an isolated system (no external force), the total momentum remains conserved.
Example: In the gun and bullet case:
Initial momentum = 0 (Rest).
Final momentum = Mass(gun)×Velocity(gun) + Mass(bullet)×Velocity(bullet) = 0.
Quick Practice & Summary
Solved Problem 1
Q: A force acts on a 5 kg object for 2s, changing velocity from 3 m/s to 7 m/s. Find Force.
Solution:
$m = 5\ kg, t = 2\ s, u = 3\ m/s, v = 7\ m/s$
Using $F = \frac{m(v-u)}{t}$:
$F = \frac{5(7 – 3)}{2}$
$F = \frac{5 \times 4}{2} = 10\ N$
Answer: 10 Newtons
Solved Problem 2
Q: Which requires more force? Accelerating 2kg at 5 m/s² OR 4kg at 2 m/s²?
Solution: Use $F = ma$
Case 1: $F_1 = 2 \times 5 = 10\ N$
Case 2: $F_2 = 4 \times 2 = 8\ N$
Since $10 > 8$, Case 1 requires more force.
Chapter Mind Map
Good Luck for Exams! 🙂