Force and Laws of Motion

Balanced and Unbalanced Forces

Understanding Motion

• Motion can be uniform (constant speed) or non-uniform (changing speed).
• We haven’t discussed what causes motion yet.

Historical Perspectives

• Earlier, it was believed that rest is the natural state of an object.
• Galileo and Newton introduced new ideas to understand motion.

What is Force?

• Force is a push, pull, or hit that changes an object’s motion.
• We don’t see force, but we see its effects.

Examples of Force

• Push a stationary object to make it move.
• Pull an object to change its direction.
• Hit an object to change its speed.

Balanced and Unbalanced Forces

Balanced Forces

• If two equal forces act in opposite directions on an object, it doesn’t move.
• Example: Pulling a block from both sides with equal force; it stays still.

Unbalanced Forces

• If two unequal forces act in opposite directions, the object moves in the direction of the stronger force.
• Example: Pulling a block with a stronger force on one side; it moves.

Friction and Movement

• Friction is the force that opposes motion.
• Example: Pushing a box on a rough floor:
  • Small push: Box doesn’t move due to friction.
  • Harder push: Still doesn’t move as friction balances the push.
  • Hardest push: Box moves because the push overcomes friction.

Riding a Bicycle

• When you stop pedaling, the bicycle slows down due to friction.
• To keep moving, you need to keep pedaling.
• An object moves at a constant speed when forces are balanced.
• To change speed or direction, an unbalanced force is needed.

Key Points to Remember

• Force is necessary to change the state of motion.
• Balanced forces don’t change motion.
• Unbalanced forces cause changes in speed or direction.
• Friction always opposes motion.
• Continuous unbalanced force changes motion, but if the force stops, the object continues with constant velocity.

Keep these points in mind to understand how forces affect the motion of objects in everyday life!

First Law of Motion

Galileo’s Observations

• Objects move with constant speed when no force acts on them.
• Examples with Marbles:
  • Marble rolls down an inclined plane: Speed increases (gravity’s force).
  • Marble climbs up: Speed decreases.
  • Marble on a frictionless plane: Rolls to the same height on the other side.
  • On a horizontal plane: Keeps moving forever (in ideal conditions with no friction).

Newton’s First Law of Motion

• Definition: An object stays at rest or in uniform motion unless acted upon by an external force.
• Inertia: Objects resist changes in their state of motion.
  • Also called the Law of Inertia.

Examples of Inertia in Everyday Life

• In a Car:
  • Sudden brake: Body moves forward (tendency to keep moving).
  • Safety belts: Slow down the forward motion to prevent injury.
• In a Bus:
  • Sudden start: Body moves backward (tendency to stay at rest).

Activities Illustrating Inertia

More About Galileo

• Early Life:
  • Born on 15 February 1564 in Pisa, Italy.
  • Interested in mathematics and natural philosophy.
  • Enrolled in medical school but shifted to mathematics.
• Scientific Contributions:
  • Wrote “The Little Balance” about finding relative densities.
  • Developed theories on motion using inclined planes.
  • Appointed professor of mathematics at the University of Padua.
• Inventions and Discoveries:
  • Developed better telescopes.
  • Designed the first pendulum clock.
  • Made astronomical discoveries: mountains on the moon, tiny stars in the Milky Way, and moons orbiting Jupiter.
  • Argued that planets orbit the Sun, not the Earth.

Inertia and Mass

• Inertia: Resistance to change in motion.
• Examples:
  • Easier to push an empty box than a full one.
  • Kicking a football vs. kicking a stone.
• Mass and Inertia:
  • Heavier objects have more inertia.
  • More mass means more resistance to change in motion.

Key Takeaways

• Inertia is a property that keeps objects at rest or in uniform motion.
• Mass measures an object’s inertia: more mass = more inertia.
• Newton’s First Law explains why objects resist changes in their motion.

Second Law of Motion

• The first law says that an unbalanced force changes an object’s velocity, causing acceleration.
• The second law explains how this acceleration depends on the force applied.

Everyday Observations

• A table tennis ball doesn’t hurt when it hits you, but a fast cricket ball does.
• A stationary truck is harmless, but a moving truck can be deadly.
• A small bullet can be lethal if fired from a gun.
• These examples show that impact depends on both mass and velocity.

Momentum

• Definition: Momentum (p) = mass (m) × velocity (v).
• Direction and Magnitude: Momentum has both direction and size, same as velocity.
• Unit: kg m/s.

Force and Momentum

• An unbalanced force changes an object’s velocity, altering its momentum.
• The force needed to change momentum depends on how long the force is applied.

Second Law of Motion

• Statement: The rate of change of momentum is proportional to the applied force in the direction of the force.

Mathematical Formulation

• If an object of mass 𝑚m moves with initial velocity 𝑢 and accelerates to velocity 𝑣 in time 𝑡 under force 𝐹:
  • Initial momentum 𝑝1=𝑚𝑢
  • Final momentum 𝑝2=𝑚𝑣
  • 
• Constant 𝑘: Chosen so that 𝑘=1, making the formula 𝐹=𝑚𝑎.
• Unit of Force: Newton (N), where 1𝑁=1𝑘𝑔×1𝑚/𝑠².

Practical Examples

• Catching a Cricket Ball:
  • Fielder pulls hands back to increase time to stop the ball.
  • This reduces acceleration and the force, preventing injury.
• High Jump:
  • Athletes fall on cushioned or sand beds to increase stopping time.
  • This reduces the rate of change of momentum and the impact force.
• Karate Chop:
  • Breaking ice with a single blow involves applying a large force in a short time, demonstrating the second law.

Connection to the First Law

• From 𝐹=𝑚𝑎:
  • If 𝐹=0, then 𝑎=0.
  • This means the object’s velocity 𝑣v doesn’t change, and it stays in its initial state, either at rest or in uniform motion.

Key Takeaways

• The second law of motion explains how force and acceleration are related.
• Momentum combines mass and velocity to describe motion.
• The law can be observed in everyday actions like catching a ball or jumping.

Examples of Second Law of Motion

Example 8.1: Calculating Force and Final Velocity

• Problem: A 5 kg object is pushed for 2 seconds, changing its velocity from 3 m/s to 7 m/s. Find the force. Then, find the final velocity if the force is applied for 5 seconds.
• Solution:
  • Given: 𝑢 = 3 m/s, 𝑣 = 7 m/s, 𝑡 = 2 s, 𝑚 = 5 kg.
  • 

Example 8.2: Comparing Forces for Different Accelerations

• Problem: Which requires more force – accelerating 2 kg at 5 m/s² or 4 kg at 2 m/s²?
• Solution:
  • Given: 𝑚1 = 2 kg, 𝑎1 = 5 m/s²; 𝑚2 = 4 kg, 𝑎2 = 2 m/s².
  • Using 𝐹=𝑚𝑎:
    • 𝐹1 = 2 kg × 5 m/s² = 10 N.
    • 𝐹2 = 4 kg × 2 m/s² = 8 N.
  • Result: 𝐹1>𝐹2​, so 2 kg at 5 m/s² needs more force.

Example 8.3: Braking Force on a Motorcar

• Problem: A car (mass along with the passengers is 1000 kg.) moving at 108 km/h stops in 4 seconds after brakes are applied. Find the force.
• Solution:
  • Given: 𝑢 = 108 km/h = 30 m/s, 𝑣 = m/s, 𝑚 = 1000 kg, 𝑡 = 4s.
  • 
  • Note: Negative sign indicates force direction is opposite to motion.

Example 8.4: Combining Masses for a Single Force

• Problem: A 5 N force gives 10 m/s² to mass 𝑚1​ and 20 m/s² to mass 𝑚2​. What acceleration is given if both masses are tied together?
• Solution:
  • Given: 𝐹 = 5N, 𝑎1 = 10m/s², 𝑎2 = 20 m/s².
  • 
  • Combined mass 𝑚=0.5+0.25=0.75m=0.5+0.25=0.75 kg.
  • 

Example 8.5: Force Exerted by Friction on a Ball

• Problem: A 20 g ball slows from 20 cm/s to rest in 10 seconds. Find the force by the table.
• Solution:
  • Given: 𝑢 = 20 cm/s = 0.2 m/s, 𝑣 = 0 m/s, 𝑡 = 10 s, 𝑚 = 20 g = 0.02 kg.
  • 
  • Using 𝐹 = 𝑚𝑎:
    • 𝐹 = 0.02 kg × − 0.02 m/s² = − 0.0004 N.
  • Note: Negative sign shows friction force is opposite to motion.

Understanding the Third Law of Motion

Understanding the Third Law of Motion

• Definition: When one object exerts a force on another, the second object exerts an equal and opposite force back.
• Key Point: Forces are equal in size but opposite in direction.
• Action and Reaction: These forces act on different objects.

Everyday Examples

• Football Collision: Two players collide, each feeling hurt due to equal and opposite forces.
• Spring Balances: Two connected spring balances show the same force reading in opposite directions.

Real-Life Applications

• Walking: When you walk, you push the ground backward, and the ground pushes you forward.
• Firing a Gun: The gun recoils because the bullet pushes it backward with an equal force.
• Sailor Jumping from a Boat: The boat moves backward when the sailor jumps forward.

Important Points

• Acceleration: Action and reaction forces may not cause the same acceleration due to different masses of objects.
• Example: A bullet accelerates more than a gun because the gun is heavier.

By understanding these simple examples and performing activities, you can see the third law of motion in action!

Chapter Summary:

• First law of motion: An object stays at rest or moves in a straight line unless acted on by an unbalanced force.
• Inertia: The tendency of objects to resist changes in their state of rest or motion.
• Mass and Inertia: Mass measures inertia. SI unit is kilogram (kg).
• Friction: Always opposes the motion of objects.
• Second law of motion: The rate of change of momentum is proportional to the applied unbalanced force and in the direction of the force.
• SI unit of force: kg m s⁻², also called newton (N). One newton force produces 1 m s⁻² acceleration on a 1 kg mass.
• Momentum: The product of mass and velocity, in the direction of the velocity. SI unit is kg m s⁻¹.
• Third law of motion: For every action, there is an equal and opposite reaction on two different bodies.