Comprehensive Study Notes on Newton's Laws of Motion

Measuring Friction: The magnitude of the force of friction can be observed through measurement readings. A smaller reading on a measuring device indicates a smaller force of friction, whereas a larger reading indicates a larger force of friction.
Friction and Velocity: Based on results from previous activities (Activity 6.1 and 6.2), it is concluded that when the force of friction is reduced, the velocity of an object decreases at a much slower rate. Consequently, the object is able to travel a larger total distance before finally coming to rest.

Ancient Scientific Beliefs: In ancient times, it was widely accepted that a force was necessary to initiate the motion of a stationary object or to halt an object that was already moving. However, for centuries, there was a misconception that a force was also required to keep an object moving at a constant velocity.
Galileo Galilei (17th Century): Galileo challenged the existing beliefs regarding motion. He argued through various thought experiments that if a body moves along a horizontal plane and all impediments (such as friction) to its motion are removed, the object will continue to move indefinitely without the need for an external force to maintain its motion.
Isaac Newton (1687): Following Galileo's work, Isaac Newton formalized these concepts into three laws of motion, published in $1687$ . This period is considered a defining moment in the history of science. Newton introduced the term "inertia" to describe an object's inherent tendency to resist changes in its state of rest or uniform motion.
SI Unit of Force: The unit of force is named the "newton" in honor of Isaac Newton.
- When the unit is written in full, it must begin with a lowercase letter ( $\text{newton}$ ).
- The symbol for the unit is always capitalized ( $N$ ).

Formal Definition: Newton's First Law of Motion states: "An object at rest remains at rest and an object in motion continues to move with a constant velocity, unless a net force acts upon the object."
Net Force and Acceleration: If the net force acting on an object is zero, the body cannot begin to move if it is at rest, nor can it change its velocity if it is in motion. In these conditions, the object's acceleration is exactly $0$ .
Understanding Constant Velocity:
- An object at rest has a velocity of zero ( $v = 0$ ).
- Constant velocity implies that there is absolutely no change in either the magnitude (speed) or the direction of the velocity.
- If a constant velocity is non-zero, the object travels in a perfectly straight line in one direction with a consistent magnitude of velocity.

Hypothesis Formation: Based on everyday experience, pushing an object gently results in low acceleration (moving slowly from rest), while a stronger push results in higher acceleration. This leads to the hypothesis: for a constant object mass, a larger force results in a larger acceleration, and a smaller force results in a smaller acceleration.
Experimental Application (Activity 6.3 - Cart and Pulley System):
- Objective: To apply forces of different magnitudes on the same object to find the resultant acceleration.
- Materials: Four ball bearing wheels, two pencils (axles), an empty cardboard box, a paper cup, a length of pipe (to act as a pulley), thread, coins/objects to act as weights, and a weighing scale to measure mass.
- Setup: Pencils are inserted through the box as axles with wheels attached. A thread is attached to the front of the cart, run over the pipe pulley at the edge of the table, and tied to a paper cup.
- Mechanism: Earth's gravitational force pulls the cup (weight) downward, which in turn pulls the cart forward with a constant force.
- Data Collection: The mass of the cup and its contents is measured on a scale. The cart is released from a start line, and its motion is recorded using slow-motion video until it reaches the end of the table.

Fundamental Principle: A force does not exist in isolation; at least two objects must interact for a force to come into play. Newton's Third Law focuses on how both interacting objects are affected.
Interaction Examples:
- Kicking a Ball: When a person kicks a ball, they apply a force to the ball, but they simultaneously feel the ball applying an equal force back onto their foot.
- Activity 6.5 (Chair and Table): While sitting on a wheeled chair with feet off the ground, pushing a heavy table forward (forward force) causes the individual in the chair to move in the opposite (backward) direction. Pulling the table toward oneself causes the chair to move forward.
Conclusion: Each time a force is applied to an object, that object applies an equal force back in the opposite direction.

Bicycling and Walking: To move forward on a bicycle without pedaling, a rider pushes the ground backward with their feet. The ground then applies an equal force in the forward direction on the rider's feet, moving the bicycle and rider forward.
Friction as a Propulsive Force: Usually, friction is thought of as a force that opposes motion. However, in walking and running, friction makes motion possible. As a person pushes the ground backward with their foot, the force of friction acts in the forward direction to prevent the foot from sliding, thus propelling the person forward.
Safety and Surface Design:
- Footwear: Grooves are added to the soles of shoes to increase the force of friction between the floor and the sole, preventing slips.
- Vehicle Tyres: Treads on tyres are designed to increase friction between the road and the rubber.
- Hazardous Surfaces: Wet polished floors, ice, or water-covered roads provide very little friction. On these surfaces, the foot or tyre attempts to push the ground/road but slips backward due to lack of grip, leading to falls or loss of vehicle control.

Thought Experiment - Frictionless Motion: Suppose an object is placed on a horizontal floor where the surfaces are so smooth that the force of friction is zero ( $f = 0$ ). If an initial velocity is given to the object, will the velocity decrease? Will it ever come to rest? This experiment demonstrates Galileo's principle: without an external force like friction, the object would continue moving forever.
Relationship and Testing: How can we use the earth's gravity to test force? Different weights (masses) result in different gravitational pulls, allowing for the application of forces of varied magnitudes to test the relationship between force and acceleration.