Overview
This lecture explains Newton's Second Law of Motion (F = ma), details the relationships between force, mass, and acceleration, and demonstrates how to solve related problems.
Newton’s Second Law: Core Concepts
- Newton's Second Law states that acceleration (a) is directly proportional to net force (F) and inversely proportional to mass (m).
- The law is usually represented as F = ma or a = F/m.
- Increasing net force increases acceleration if mass is constant.
- Increasing mass decreases acceleration if net force is constant.
- Acceleration and force are directly proportional; acceleration and mass are inversely proportional.
Proportional Changes and Problem-Solving
- If net force doubles, acceleration doubles (if mass is unchanged).
- If mass doubles, acceleration halves (if net force is unchanged).
- Acceleration changes by the factor (factor of force increase)/(factor of mass increase).
- Replace unchanged quantities with 1 when calculating factors.
Direction of Force and Acceleration
- Acceleration always points in the same direction as the net force.
- When solving vector problems, the sign indicates direction (negative for left/west, positive for right/east).
- The magnitude of a force is always positive; direction is specified separately.
Worked Examples
- Example 1: A 5 kg block on a frictionless surface with a 40 N force has an acceleration of 8 m/s² in the direction of the force.
- Example 2: An 8 kg block with a 35 N applied force west and 19 N friction east: Net force is 16 N west; acceleration = 2 m/s² west.
- To solve for net force, sum all forces (considering direction/signs), then use F = ma for acceleration.
Force & Velocity Directions
- Force and velocity in same direction: object speeds up (accelerates).
- Force opposite velocity: object slows down (decelerates).
- Force perpendicular to velocity: object turns but does not change speed at that instant.
Additional Sample Problems
- To find average force accelerating a block: use kinematics to find acceleration, then F = ma.
- Car braking example: convert units as needed, use kinematics to find deceleration, then F = ma (force is negative/opposite direction).
Key Terms & Definitions
- Newton's Second Law — F = ma; the net force on an object equals mass times acceleration.
- Net Force — The sum of all forces acting on an object, considering direction.
- Acceleration (a) — Change in velocity per unit time; SI unit: m/s².
- Direct Proportion — Both quantities increase or decrease together.
- Inverse Proportion — One quantity increases as the other decreases.
- Magnitude — The absolute value (size) of a vector, always positive.
Action Items / Next Steps
- Practice solving F = ma problems with varying force and mass.
- Review kinematic equations for motion calculations.
- Convert units as necessary (e.g., mph to m/s) in problem-solving tasks.