Unit 5.3 – Free Fall

• A ball dropped from a height falls straight down because of gravity.
• A skydiver jumping out of a plane initially experiences free fall before air resistance becomes significant.

Key Points About Free Fall

1. Acceleration in Free Fall:
   • During free fall, all objects accelerate at the same rate, regardless of their mass.
   • Near the Earth's surface, this acceleration is $𝑔=9.8{\text{m/s}}^2$.
2. No Air Resistance:
   • In true free fall, there is no air resistance or other external forces.
   • This means that even a feather and a rock would fall at the same speed if there were no air to slow them down.
3. Initial Velocity:
   • If an object is simply dropped, its initial velocity ($𝑢$) is zero.
   • If the object is thrown downward, it has a nonzero initial velocity.
4. Equations of Motion:
   The same equations of motion used for uniformly accelerated motion apply to free fall. These are:
   • $𝑣=𝑢+𝑔\cdot 𝑡$
   • $𝑠=𝑢\cdot 𝑡+\frac{1}{2}𝑔\cdot {𝑡}^2$
   • ${𝑣}^2={𝑢}^2+2\cdot 𝑔\cdot 𝑠$
   Where:
   • $𝑢$: Initial velocity ($\text{m/s}$)
   • $𝑣$: Final velocity ($\text{m/s}$)
   • $𝑡$: Time of fall ($\text{s}$)
   • $𝑠$: Distance fallen ($\text{m}$)
   • $𝑔$: Acceleration due to gravity ($9.8{\text{m/s}}^2$)

Detailed Notes with Bullets

1. Why Do All Objects Fall at the Same Rate?

• Gravity pulls on every object equally, depending only on its mass.
• Heavier objects experience more gravitational force, but they also have more inertia (resistance to motion), which balances out the effect.
• Example: A bowling ball and a tennis ball dropped from the same height will hit the ground at the same time if there’s no air resistance.

2. What Happens When Air Resistance is Present?

• In real life, air resistance slows down lighter objects like feathers more than heavier ones like rocks.
• Without air resistance (e.g., in a vacuum), all objects fall at the same rate.
• Example: On the Moon, where there is no air, a hammer and a feather fall at the same speed.

3. How Does Free Fall Work?

• When you drop an object, it starts with zero velocity and gains speed as it falls.
• Every second, its velocity increases by $9.8\text{m/s}$.
• After 1 second, the velocity is $9.8\text{m/s}$.
• After 2 seconds, the velocity is $19.6\text{m/s}$, and so on.

4. Calculating Distance Fallen

• The distance an object falls depends on how long it has been falling.
• Formula:
  $$𝑠=\frac{1}{2}𝑔\cdot {𝑡}^2$$
  Example:
  • After 1 second, the object falls:
  $$𝑠=\frac{1}{2}\cdot 9.8\cdot (1{)}^2=4.9\text{m}$$
  • After 2 seconds, the object falls:
  $$𝑠=\frac{1}{2}\cdot 9.8\cdot (2{)}^2=19.6\text{m}$$

Quick Review, Exam Tips, Tricks & Traps

Key Points to Remember

• Free fall is motion under gravity alone, with no air resistance.
• All objects, regardless of mass, fall at the same rate ($𝑔=9.8{\text{m/s}}^2$) in free fall.
• Use equations of motion to solve problems involving free fall.

Exam Tips

1. Always check if the question involves free fall (no air resistance) or real-life fall (with air resistance).
2. Use the correct value of $𝑔=9.8{\text{m/s}}^2$ unless the question specifies otherwise.
3. For objects dropped from rest, use $𝑢=0$ in the equations of motion.

Common Traps

1. Students often forget that air resistance affects real-life falls but not free fall.
2. Misinterpreting the role of mass: Mass does not affect the rate of free fall.

Tricks for Competitive Exams

1. Look for keywords like "dropped," "falling freely," or "vacuum" to identify free fall scenarios.
2. In MCQs, eliminate options where heavier objects fall faster—it’s impossible in free fall.
3. Use shortcuts:
   • Distance fallen after $𝑡$ seconds: $𝑠=\frac{1}{2}𝑔\cdot {𝑡}^2$.
   • Velocity after $𝑡$ seconds: $𝑣=𝑔\cdot 𝑡$.

Quick Recall Table

Additional Content: Real-Life Examples and Applications

1. Dropping Objects

• When you drop a stone from a bridge, it accelerates downward at $9.8{\text{m/s}}^2$.
• The longer it falls, the faster it moves.

2. Skydiving

• Skydivers initially experience free fall until air resistance builds up and balances the force of gravity, leading to terminal velocity.

3. Space Exploration

• Astronauts train for space missions in environments that simulate free fall, such as parabolic flights or underwater simulations.

4. Experiments in Vacuum

• Experiments in vacuum chambers show that objects like feathers and hammers fall at the same rate, proving that air resistance is the reason for differences in real-life falls.