PHY 109: Forces and Newton's Laws (Part 1)

Introduction to Forces and Newton\'s Laws

• Instructor: Shadman Salam (DMSS)
• Course: PHY 109
• Institution: East West University
• Lecture Subject: Forces and Newton\'s Laws (Part 1)

Definition and Properties of Force

• Conceptual Definition: In everyday language, a force is defined as a push or a pull.
• Units of Measurement: The SI unit of force is the Newton ($N$). One Newton is defined as:     $N = kg\,m/s^2$
• Primary Properties:
  • Force as Interaction: A force is always the result of an interaction between two distinct objects.
  • Analysis Requirements: For every specific force identified, one must identify what causes the force and which object the force acts upon.
  • Vector Nature: Force is a vector quantity, meaning it possesses both magnitude and direction.

Classification of Forces

• Non-contact Forces: These are forces that act at a distance without physical contact. The primary example given is:
  • Gravity: Described as an "action" force at a distance.
• Contact Forces: These occur when objects are physically "touching" each other. Examples include:
  • Normal Force: This force acts perpendicular to the surface of contact.
  • Friction Force: This force acts parallel to the surface of contact.
  • Drag Force: This involves the interaction between an object and air or other fluids.
  • Tension Force: The pull exerted by a string, rope, or chain.

Newton’s First Law (Law of Inertia)

• Formal Statement: Every object continues in its state of rest, or of uniform motion in a straight line, as long as no net force acts on it.
• Conditions for Validity:
  • The law is only valid in an inertial reference frame.
  • Inertial Reference Frame: A reference frame that is not accelerating with respect to another reference frame.
  • Earth as a Frame: The Earth is considered to be approximately an inertial reference frame.
• Frame of Reference Definition: Consists of a coordinate system combined with a time scale.
• Educational Resource: The lecture references a simulation for Newton\'s First Law available at: https://phet.colorado.edu/sims/html/forces-and-motion-basics/latest/forces-and-motion-basics_all.html.

Mass and Inertia

• Inertia Definition: The measure of the force required to change an object\'s state of motion.
• Mass: Mass is the quantitative measure of inertia.
  • Relationship: Objects with large inertia (large mass) require a larger force to achieve the same change in their state of motion compared to lighter objects.
• SI Unit of Mass: Kilograms ($kg$).
• Change in Motion: Any change in the state of motion is formally described as an acceleration.
• Comparative Reference: The relationship between mass and inertia is illustrated through a video link: https://youtu.be/E43-CfukEgs?t=78.

Review of Motion Concepts

• Average Velocity: Calculated via the slope of a position-time graph over a specific interval:     $\text{Slope} = \frac{\Delta x}{\Delta t}$
• Instantaneous Velocity: The velocity of an object at a specific point in time:     $v(t) = \frac{d}{dt}x(t) = \text{Slope}$
• Acceleration: Defined as the change in velocity over ("per") the change in time. Acceleration is a vector quantity.
  • Average Acceleration:         $\mathbf{a}_{average} = \frac{\Delta \mathbf{v}}{\Delta t} = \frac{\mathbf{v}(t_f) - \mathbf{v}(t_i)}{t_f - t_i}$
  • Instantaneous Acceleration:         $\mathbf{a} = \frac{d}{dt}\mathbf{v}(t) = \frac{d}{dt}\left(\frac{d}{dt}\mathbf{x}(t)\right) = \frac{d^2}{dt^2}\mathbf{x}(t)$

Properties of Acceleration

• Types of Change: Acceleration can refer to a change in speed, a change in direction, or both.
• Direction: Acceleration is a vector directed in the same direction as the change in velocity ($\Delta \mathbf{v}$).
• Distinction from Motion: Acceleration is not always in the same direction as the direction of motion.
  • Example: As a Dhaka Metro rail train slows down coming into a station, its acceleration is in the opposite direction to its motion ($\mathbf{v}$ and $\mathbf{a}$ point in opposite directions).
• Speed Variations:
  • If $\mathbf{a}$ is in the same direction as $\mathbf{v}$, the object speeds up.
  • In one dimension, an object with negative acceleration may be slowing down or speeding up, depending entirely on the direction of initial velocity.
  • Critical Distinction: Negative acceleration is not inherently the same as deceleration.

Newton’s Second Law of Motion

• Formal Statement: The acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass.
• Direction: The direction of acceleration is always in the direction of the net force acting on the object.
• Mathematical Expression:     $\mathbf{a} = \frac{\Sigma \mathbf{F}}{m}$     This is usually written as:     $\Sigma \mathbf{F} = m\mathbf{a}$
• Vector Components: Since this is a vector equation, it implies three scalar equations:
  1. $\Sigma F_x = m a_x$
  2. $\Sigma F_y = m a_y$
  3. $\Sigma F_z = m a_z$

Questions & Discussion

• Question 1 (Rocket Ship): A rocket ship in space has its engines firing and is following a path (Path 1). At point 2, the engines shut off. Which path does the rocket ship follow?

  • Answer: Path B. According to the Law of Inertia, without a net force (engines off), the object maintains its state of uniform motion in a straight line.

• Question 2 ("Frictionless Truck" - Ground Observer): A box sits in the back of a truck with no friction between the box and the truck. To a person standing on the ground, when the truck accelerates right, how does the box move?

  • Answer: The box does not move initially. Because $\Sigma \mathbf{F} = 0$ for the box, and its initial velocity was zero (relative to ground), it stays at rest while the truck moves out from under it.

• Question 3 ("Frictionless Truck" - Truck Observer): To a person on the truck, how does the box move?

  • Answer: The box appears to accelerate backwards. This occurs because the truck is a Non-Inertial Reference Frame ($\Delta v \neq 0$), where the observer experiences acceleration and perceives the stationary box as moving.

• Question 4 (Equal and Opposite Forces): An object has two forces of equal magnitude but opposite direction applied to it. Which is true?

  • Answer: None of the above (E). The object might be moving right, left, up, down, or not moving at all. Newton\'s First Law tells us only that there is no change in motion ($\mathbf{a} = 0$), not what the current velocity is.

• Question 5 (Unequal Opposite Forces): An object has two forces of different magnitude but opposite direction applied to it (e.g., a larger force to the right, smaller to the left). What is true about the object at the instant shown?

  • Answer: The object must be accelerating to the right (A). While we do not know its current direction of movement (velocity), Newton\'s Second Law states that acceleration must follow the direction of the net force.