13
Free fall of bodies
Textbook: pp. 48–49
GoalKnow free fall and the formulas υ = gt and h = gt²/2.
New words
free fall · erkin tushishacceleration of free fall g · erkin tushish tezlanishi gair resistance · havo qarshiligivacuum · vakuum
Explanation
The motion of a body falling under the Earth’s gravity alone, without air resistance, is called free fall. In a vacuum all bodies — a stone and a feather alike — fall with the same acceleration. This is the acceleration of free fall, denoted g; near the Earth’s surface g ≈ 9.8 m/s². In problems we take g = 10 m/s² to make calculations easier (as the textbook does). For a body falling from rest, υ = gt and h = gt²/2. In ordinary air light bodies (paper, a feather) fall more slowly because of air resistance.
Worked examples
A stone falling for 3 s (g = 10 m/s²): υ = 10 · 3 = 30 m/s, height h = 10 · 3² : 2 = 45 m.
For a body dropped from 20 m, h = gt²/2 gives t² = 2 · 20 : 10 = 4, so t = 2 s (2 · 2 = 4); it lands with υ = 10 · 2 = 20 m/s.
Class activity
“Paper and notebook”: with an adult, drop a flat sheet and a notebook together from a low height, then a crumpled sheet; explain the difference by air resistance. Safety: do not climb on chairs; keep the height under 1.5 m.
Practice
1
What is free fall?
Falling under gravity alone, without air resistance.
2
A body falls from rest for 4 s (g = 10 m/s²). Velocity (m/s)?
40
3
A body falls from rest for 2 s (g = 10 m/s²). How many metres?
20
4
Why does a feather fall slower than a stone in air but equally in a vacuum?
In air the feather feels large air resistance; in a vacuum there is none and both accelerate at g.