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Free-Falling Objects Overview

• Title: Free-Falling Objects

• Source: Quipper

Learning Competencies

• Students will learn to:

  • Describe the horizontal and vertical motions of a projectile (S9FE-IVa-34).

Learning Objectives

• By the end of this lesson, students should be able to:

  • Describe uniformly accelerated motion (UAM).

  • Describe free-falling objects.

  • Solve problems using UAM equations and concepts related to free-falling objects.

Key Concepts in Mechanics

Mechanics

• The study of motion and forces affecting the motion of objects.

Kinematics

• The motion of objects without reference to forces acting on them.

Dynamics

• Focus on forces and their influence on motion.

Kinematics Equations

• **Equations of motion for uniformly accelerated objects: **

  • Distance: ( d = v_i t + \frac{1}{2} a t^2 )

  • Final velocity squared: ( v_f^2 = v_i^2 + 2ad )

  • Final velocity: ( v_f = v_i + at )

  • Average speed: ( \bar{v} = \frac{(v_f + v_i)}{2} )

Scalar and Vector Quantities

Scalar Quantities

• Describes quantities with magnitude but no direction.

  • Examples: time, speed, energy, distance, temperature.

Vector Quantities

• Describes quantities with both magnitude and direction.

  • Examples: displacement, velocity, acceleration.

Definitions of Key Terms

Displacement (Δx or Δs)

• Change in position of an object; a vector quantity.

  • Unit: meters (m)

Velocity (𝑣)

• Distance traveled per unit time in a specific direction; rate of change of displacement.

  • Unit: meters per second (m/s)

  • Average velocity: ( v_{avg} = \frac{Δx}{Δt} )

Acceleration (𝑎)

• Rate of change of velocity over time; a vector quantity.

  • Unit: meters per second squared (m/s²)

  • Formula: ( a = \frac{Δv}{Δt} )

Time (𝑡)

• A measure of the duration of motion; a scalar quantity.

  • Unit: seconds (s)

Motion of Falling Objects

Free Fall Motion

• Example of a bungee jumper descending until the cord becomes taut.

• Objects in free fall are influenced solely by gravity, neglecting air resistance.

Galileo's Contributions

• Known for his studies of motion and free fall, using inclined planes for experiments to reduce acceleration.

• Demonstrated that all objects fall toward the earth at the same rate regardless of mass when air resistance is negligible.

Understanding Free Fall Motion

• When an object falls freely, its velocity increases at a uniform rate under the influence of gravity.

• Air resistance is minimal, and only gravity acts on the object.

• Direction of velocity is considered downward (negative direction).

Air Resistance

• A frictional force that opposes the motion of falling objects.

• Increases with the speed of the object and the surface area.

• Skydivers use parachutes to slow down with increased air resistance.

Problem-Solving Tips

• Always check for consistency of units.

• Isolate the unknown variable before substituting given values into the equations.

Equations for Free Fall Motion

1. Final velocity equation: ( v_f = v_i + gt )

2. Displacement equation: ( y = v_i t + \frac{1}{2}gt^2 )

3. Final velocity squared: ( v_f^2 = v_i^2 + 2gy )

Example Problems

Example: Pen Dropped

1. Identify: Calculate the final velocity (v_f) of a pen dropped from a height of 5 m.

2. Given: Initial velocity, gravity, height.

3. Equate: Find final velocity.

4. Result: Final velocity = 9.90 m/s downward.

Example: Tennis Ball

1. Identify: Calculate height from which a tennis ball was thrown down.

2. Given: Initial and final velocities provided.

3. Equation: Write corresponding equation.

4. Results: Height determined to be 2.98 m.

Key Points Summary

• UAM occurs when an object experiences constant acceleration.

• Free Fall Motion is influenced solely by gravity, undergoes constant acceleration of -9.8 m/s².

• All objects fall at the same rate if air resistance is ignored.

• Air Resistance opposes motion; increases with speed and surface area.