Understanding force, Newton's laws, momentum, and conservation principles
Force is a push or pull that can change or tend to change the state of rest or uniform motion of an object. Force is a vector quantity (has both magnitude and direction).
Force is like the "effort" you make to change something! When you push a door open, you apply force. When you pull a drawer, you apply force. When you kick a football, you apply force. Force is what makes things start moving, stop moving, or change direction!
Force can produce following effects:
1. Change in state of motion:
β’ Can make a stationary object move (pushing a cart)
β’ Can stop a moving object (catching a ball)
β’ Can change speed of a moving object (accelerating a car)
2. Change in direction:
β’ Can change the direction of a moving object (hitting a ball with
bat)
3. Change in shape or size:
β’ Can deform objects (squeezing a sponge, stretching a rubber
band)
β’ Kicking a football β Force changes state from rest to motion
β’ Catching a ball β Force stops the moving ball
β’ Hitting a tennis ball β Force changes direction
β’ Pressing a spring β Force changes shape
β’ Opening a door β Force causes rotation
β’ Lifting a bag β Force opposes gravity
Forces that act only when objects are in physical contact.
Examples:
β’ Muscular Force: Force applied by muscles
(pushing, pulling, lifting)
β’ Friction: Force that opposes motion between
surfaces in contact
β’ Normal Force: Force perpendicular to surface
(book on table)
β’ Tension: Force transmitted through rope,
string, or cable
β’ Spring Force: Force exerted by compressed or
stretched spring
Forces that act without physical contact.
Examples:
β’ Gravitational Force: Attraction between any two
masses (Earth attracts objects)
β’ Magnetic Force: Attraction or repulsion between
magnets
β’ Electrostatic Force: Attraction or repulsion
between charged objects
When two or more forces acting on an object cancel each other out, resulting in zero net force. The object remains in its state of rest or uniform motion.
β’ A book lying on a table (weight balanced by normal force)
β’ Tug of war with equal teams (rope doesn't move)
β’ A car moving at constant speed (driving force equals
friction)
β’ A person standing still (weight balanced by ground reaction)
When forces acting on an object do not cancel out, resulting in a net force. The object's state of motion changes (acceleration occurs).
β’ Pushing a stationary cart (cart starts moving)
β’ Applying brakes to a car (car slows down)
β’ Falling apple (gravity not balanced by any upward force)
β’ Tug of war with unequal teams (rope moves toward stronger team)
Newton's First Law: An object at rest remains at rest, and an object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced external force.
Objects are "lazy"! They don't like to change what they're doing.
A resting object wants to keep resting. A moving object wants to
keep moving in the same way. They only change when forced to
change!
It's like you relaxing on a couch - you don't want to get up
unless someone forces you to (like your mom calling for dinner)!
Inertia is the natural tendency of an object to resist any change in its state of rest or uniform motion. It is the property of matter to remain in its existing state.
1. Inertia of Rest: Tendency to remain at rest
Example: When a bus suddenly starts, passengers jerk backward
2. Inertia of Motion: Tendency to remain in
motion
Example: When a bus suddenly stops, passengers jerk forward
3. Inertia of Direction: Tendency to maintain
direction of motion
Example: When a bus takes a turn, passengers lean outward
Inertia of Rest:
β’ Shaking a tree to make fruits fall (fruits at rest want to stay
at rest)
β’ Beating a carpet to remove dust (dust wants to stay at rest)
β’ Pulling a tablecloth quickly from under dishes (dishes stay in
place)
Inertia of Motion:
β’ Athlete cannot stop immediately after finishing race
β’ We fall forward when we trip (body wants to keep moving)
β’ Seat belts in cars (prevent forward motion during sudden
stop)
Inertia of Direction:
β’ Mud flying off bicycle tire (mud wants to move in straight
line)
β’ Centrifuge separating cream from milk (heavier particles move
outward)
A truck has much more mass than a bicycle, so it has much more inertia. Greater inertia means it resists changes in motion more strongly. That's why you need more force to start moving a truck (or to stop it once it's moving)!
Newton's Second Law: 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.
F = ma
Where:
F = Force (Newton, N)
m = Mass (kilogram, kg)
a = Acceleration (m/sΒ²)
Or: Force = Mass Γ Acceleration
1 Newton (N): Force that produces an acceleration
of 1 m/sΒ² in a mass of 1 kg
1 N = 1 kg Γ 1 m/sΒ² = 1 kgβ
m/sΒ²
A force of 20 N is applied to an object of mass 4 kg. Find the
acceleration produced.
Solution:
Given: F = 20 N, m = 4 kg
Using F = ma
20 = 4 Γ a
a = 20/4 = 5 m/sΒ²
The object accelerates at 5 m/sΒ².
A cricket ball of mass 150 g moving at 12 m/s is brought to rest
by a player in 0.1 seconds. Find the force applied.
Solution:
Mass (m) = 150 g = 0.15 kg
Initial velocity (u) = 12 m/s
Final velocity (v) = 0 m/s
Time (t) = 0.1 s
First find acceleration:
a = (v - u)/t = (0 - 12)/0.1 = -120 m/sΒ²
(Negative sign indicates deceleration)
Now find force:
F = ma = 0.15 Γ (-120) = -18 N
Force applied is 18 N in opposite direction of motion.
Think of pushing a shopping cart:
β’ Empty cart (small mass) β Easy to push β Large acceleration with
small force
β’ Full cart (large mass) β Hard to push β Small acceleration with
same force
To get the same acceleration for a full cart, you need to push
much harder (apply more force)!
Momentum is the quantity of motion possessed by a moving object. It is the product of mass and velocity. Momentum is a vector quantity.
Momentum (p) = Mass Γ Velocity
p = m Γ v
Where:
p = Momentum (kgβ
m/s)
m = Mass (kg)
v = Velocity (m/s)
SI unit: kilogram meter per second (kgβ
m/s) or Newtonβ
second (Nβ
s)
A car of mass 1000 kg is moving at 20 m/s. Calculate its
momentum.
Solution:
Mass (m) = 1000 kg
Velocity (v) = 20 m/s
Momentum (p) = m Γ v
p = 1000 Γ 20
p = 20,000 kgβ
m/s
The car has momentum of 20,000 kgβ
m/s in the direction of motion.
Momentum is like the "oomph" or "impact force" of a moving
object!
β’ A heavy truck moving slowly has large momentum (large mass)
β’ A bullet moving very fast has large momentum (large velocity)
β’ Both are hard to stop!
Catching a tennis ball is easy, but catching a cricket ball moving
at same speed is harder because cricket ball has more mass, hence
more momentum!
Force = Rate of change of momentum
F = (Final momentum - Initial momentum) / Time
F = (mv - mu) / t
F = m(v - u) / t
F = ma
This shows that Newton's Second Law can be stated as: Force equals
rate of change of momentum.
When jumping from a height, our momentum must become zero when we
land.
Change in momentum is fixed: Ξp = mv - 0 = mv
Force F = Ξp / t
By bending knees, we increase the time (t) of landing.
Since F = Ξp / t, increasing t decreases F.
Less force means less impact, less chance of injury! This is why
we should bend our knees when landing from a jump.
Same principle! Rolling increases the time of impact, which decreases the force experienced. This prevents injuries during high jumps or pole vaults.
Newton's Third Law: For every action, there is an equal and opposite reaction. Forces always occur in pairs - action and reaction forces.
Forces are like conversations - there's always a two-way exchange! When you push someone, they automatically push back on you (even if they don't mean to). You can't have a one-sided push - physics doesn't allow it!
1. Walking:
β’ Action: You push ground backward with your foot
β’ Reaction: Ground pushes you forward
β’ Result: You move forward!
2. Swimming:
β’ Action: You push water backward with hands
β’ Reaction: Water pushes you forward
β’ Result: You swim forward!
3. Rocket Propulsion:
β’ Action: Rocket pushes hot gases downward
β’ Reaction: Gases push rocket upward
β’ Result: Rocket lifts off!
4. Gun Recoil:
β’ Action: Gun pushes bullet forward
β’ Reaction: Bullet pushes gun backward
β’ Result: Gun recoils backward!
5. Rowing a Boat:
β’ Action: Oar pushes water backward
β’ Reaction: Water pushes boat forward
β’ Result: Boat moves forward!
6. Jumping from Boat:
β’ Action: You push boat backward
β’ Reaction: Boat pushes you forward
β’ Result: You jump forward, boat moves backward!
According to Newton's third law, when you push Earth backward,
Earth pushes you forward with equal force. But why doesn't Earth
move?
Actually, it does! But Earth has HUGE mass compared to you.
Using F = ma:
β’ Same force acts on you and Earth
β’ Your mass is small β You get large acceleration β You move
noticeably
β’ Earth's mass is enormous β Earth gets tiny acceleration β
Movement is undetectable
The acceleration of Earth is so small that we cannot observe it!
Law of Conservation of Momentum: In an isolated system (no external forces), the total momentum before any interaction equals the total momentum after the interaction. Momentum is conserved.
Total momentum before collision = Total momentum after
collision
mβuβ + mβuβ = mβvβ + mβvβ
Where:
mβ, mβ = masses of two objects
uβ, uβ = initial velocities
vβ, vβ = final velocities
Momentum is like money in a closed economy! Money can be transferred between people, but the total amount of money stays the same. Similarly, momentum can be transferred between objects during collision, but total momentum remains constant!
Consider two objects A and B colliding:
Before collision:
β’ Object A: mass = mβ, velocity = uβ
β’ Object B: mass = mβ, velocity = uβ
After collision:
β’ Object A: velocity = vβ
β’ Object B: velocity = vβ
During collision, let Fβ be force on A by B, and Fβ be force on B
by A.
By Newton's third law: Fβ = -Fβ
For object A: Fβ = mβ(vβ - uβ)/t
For object B: Fβ = mβ(vβ - uβ)/t
Since Fβ = -Fβ:
mβ(vβ - uβ)/t = -mβ(vβ - uβ)/t
mβ(vβ - uβ) = -mβ(vβ - uβ)
mβvβ - mβuβ = -mβvβ + mβuβ
mβvβ + mβvβ = mβuβ + mβuβ
This proves: Total momentum after = Total momentum
before
A 5 kg object moving at 4 m/s collides with a 3 kg object moving
at 2 m/s in opposite direction. After collision, they stick
together. Find their common velocity.
Solution:
mβ = 5 kg, uβ = 4 m/s (let's say positive direction)
mβ = 3 kg, uβ = -2 m/s (opposite direction, so negative)
After collision: common velocity = v
Using conservation of momentum:
mβuβ + mβuβ = (mβ + mβ)v
5(4) + 3(-2) = (5 + 3)v
20 - 6 = 8v
14 = 8v
v = 1.75 m/s
They move together at 1.75 m/s in the direction of the 5 kg
object.
A gun of mass 4 kg fires a bullet of mass 50 g at 400 m/s. Find
the recoil velocity of gun.
Solution:
Gun mass (M) = 4 kg
Bullet mass (m) = 50 g = 0.05 kg
Bullet velocity (v) = 400 m/s
Recoil velocity of gun = V
Initially both are at rest, so initial momentum = 0
Using conservation of momentum:
Initial momentum = Final momentum
0 = mv + MV
0 = 0.05(400) + 4(V)
0 = 20 + 4V
4V = -20
V = -5 m/s
Gun recoils backward at 5 m/s (negative sign shows opposite
direction).
Rockets work on conservation of momentum!
β’ Initially, rocket + fuel system is at rest (total momentum =
0)
β’ Fuel burns and hot gases are expelled backward with high
velocity
β’ To conserve momentum (keep total = 0), rocket must move
forward
β’ Mass of gases Γ velocity backward = Mass of rocket Γ velocity
forward
This is why rockets can work in space where there's no air to push
against!
Why does a gun kick backward when fired?
Before firing: Total momentum = 0 (both gun and bullet at rest)
After firing: Bullet goes forward (gains positive momentum)
To keep total momentum = 0, gun must go backward (gain negative
momentum)!
Since bullet has small mass but high velocity, gun has large mass
but small velocity. But their momentums are equal and opposite!
Safety tip: Hold gun firmly against shoulder to
reduce recoil impact!
Newton's Laws Summary:
1st Law: "Objects are lazy - they don't like to
change!"
(Inertia - resistance to change)
2nd Law: "Push harder or use lighter object to
move faster!"
(F = ma - more force or less mass gives more acceleration)
3rd Law: "Every push has a push-back!"
(Action = Reaction, but on different objects)
Q: Which would require a greater force -
accelerating a 2 kg mass at 5 m/sΒ² or a 4 kg mass at 2 m/sΒ²?
Solution:
For 2 kg mass: Fβ = ma = 2 Γ 5 = 10 N
For 4 kg mass: Fβ = ma = 4 Γ 2 = 8 N
Answer: Accelerating 2 kg mass at 5 m/sΒ² requires
greater force (10 N vs 8 N).
Q: A car of mass 1500 kg changes its velocity
from 36 km/h to 72 km/h in 10 seconds. Calculate the force
applied.
Solution:
m = 1500 kg
u = 36 km/h = 36 Γ (5/18) = 10 m/s
v = 72 km/h = 72 Γ (5/18) = 20 m/s
t = 10 s
Acceleration: a = (v - u)/t = (20 - 10)/10 = 1 m/sΒ²
Force: F = ma = 1500 Γ 1 = 1500 N
Answer: Force applied is 1500 N.
Q: Why are passengers thrown forward when a bus
suddenly stops?
Answer: When bus is moving, passengers are also
moving with the bus. When bus stops suddenly, lower part of
passenger's body (in contact with seat) stops with the bus due to
friction. But upper part continues to move forward due to inertia
of motion. This causes passengers to jerk forward. This is inertia
of motion.
Q: Calculate momentum of a 10 kg object moving at
12 m/s.
Solution:
Mass (m) = 10 kg
Velocity (v) = 12 m/s
Momentum (p) = m Γ v = 10 Γ 12 = 120 kgβ
m/s
Answer: Momentum is 120 kgβ
m/s.
Q: A 50 kg boy and a 40 kg girl are standing on a
frictionless frozen lake. The boy pushes the girl, giving her
velocity of 1 m/s. What is the boy's velocity?
Solution:
Initial momentum = 0 (both at rest)
Boy's mass (mβ) = 50 kg
Girl's mass (mβ) = 40 kg
Girl's velocity (vβ) = 1 m/s
Boy's velocity = vβ
Using conservation of momentum:
0 = mβvβ + mβvβ
0 = 50(vβ) + 40(1)
50vβ = -40
vβ = -0.8 m/s
Answer: Boy moves at 0.8 m/s in opposite
direction (negative sign indicates opposite direction).
Q: Explain why it is difficult to walk on sand or
ice.
Answer: Walking depends on friction between foot
and ground. When we walk:
β’ Action: We push ground backward
β’ Reaction: Ground pushes us forward (this requires friction)
On sand or ice, friction is very less. Ground cannot provide
enough reaction force. So we slip instead of moving forward. This
makes walking difficult.
For F = ma problems:
1. Convert all units to SI units (kg, m/s, m/sΒ²)
2. Convert km/h to m/s by multiplying with 5/18
3. First find acceleration using: a = (v - u)/t
4. Then find force using: F = ma
For momentum problems:
1. Calculate initial momentum: pβ = mβuβ + mβuβ
2. Calculate final momentum: pβ = mβvβ + mβvβ
3. Use: pβ = pβ (conservation)
4. Watch out for direction (opposite = negative)
Remember: Always write units in your answer!