Acceleration due to Gravity ഭൂഗുരുത്വാകർഷണത്വരണം
A force that keeps acting makes an object speed up – it gives it an acceleration (ത്വരണം). The Earth's pull keeps acting on every falling object. So how fast does a falling object speed up? Does a heavy stone speed up faster than a light one? Here you find the famous number g = 9.8 m/s² and see why heavy and light things fall together.
- Newton's second law: F = ma (force = mass × acceleration).
- Acceleration is measured in m/s² (speed gained in m/s every second). Free fall from rest: s = ½ a t², v = a t.
- Page 6: F = G m1m2/d², with G = 6.67 × 10−11 N m²/kg².
1. Why does a coconut fall? (Fig 4.7)
ഭൂമിയുടെ ആകർഷണബലം കാരണമല്ലേ തെങ്ങിൽ നിന്നും ഞെട്ടറ്റുപോയ തേങ്ങ താഴോട്ട് തന്നെ പതിക്കുന്നത്? A coconut that breaks off its stalk falls straight down because of the Earth's pull. Nothing balances that pull, so it is an unbalanced force (അസന്തുലിത ബലം), and an unbalanced force produces acceleration. Watch the coconut's position every 0.25 s.
The gaps between the images grow: in each quarter-second the coconut covers more distance than in the one before. That is what acceleration looks like.
A coconut (about 1.5 kg) falling from a 15 m tree reaches about 17 m/s – over 60 km/h – in under 2 seconds. Never stand or park under a coconut tree with ripe nuts, especially on a windy monsoon day.
2. Activity – drop a light and a heavy object together
ഒരു നിശ്ചിത ഉയരത്തിൽ നിന്ന് മാസ് കുറഞ്ഞ വസ്തുവും മാസ് കൂടിയ വസ്തുവും ഒരുമിച്ചു താഴേക്ക് പതിപ്പിക്കുക. – From the same height, let a light object and a heavy object fall together (textbook page 77).
| Height (m) | Air | Iron ball 2 kg: time (s) | Plastic ball 3 g: time (s) |
|---|
Model: without air both follow s = ½ g t² exactly. With air, air resistance grows with speed; it hardly matters for the iron ball but holds back the very light ball (which can never go faster than about 9 m/s). Try 5 m and 50 m with air ON.
Q. ഏതാണ് ആദ്യം എത്തിയത്? – Which one reached the ground first?
Q. ഏതിനായിരിക്കും കൂടുതൽ ത്വരണം ഉണ്ടായത്? – Which one had more acceleration?
By Newton's second law F = ma. If F is the Earth's attractive force and m the mass of the object, then a is the acceleration caused by the Earth's attraction:
ഭൂഗുരുത്വാകർഷണബലത്താൽ വസ്തുക്കൾക്കുണ്ടാവുന്ന ത്വരണം ഭൂഗുരുത്വാകർഷണത്വരണം (acceleration due to gravity) എന്ന് അറിയപ്പെടുന്നു. ഇത് g എന്ന അക്ഷരം കൊണ്ടാണ് സൂചിപ്പിക്കുന്നത്.
The acceleration produced in objects by the Earth's gravitational force is called the acceleration due to gravity. It is written with the letter g.
3. A formula for g (Fig 4.8)
Q. g യുടെ യൂണിറ്റെന്ത്? – What is the unit of g?
Q. ഈ സമവാക്യത്തിൽ വസ്തുവിന്റെ മാസ് ഉൾപ്പെട്ടിട്ടുണ്ടോ? – Is the mass of the object in this equation?
തെങ്ങിലുള്ള തേങ്ങയിലേക്ക് ഭൂകേന്ദ്രത്തിൽ നിന്നുള്ള ദൂരം എങ്ങനെ കണക്കാക്കാം? Strictly, the distance is the Earth's radius plus the height of the tree: R + h. But R is so large (6400 km = 64,00,000 m) that adding about 15 m makes no noticeable difference.
Check: with R = 6.4 × 106 m, g = 9.77051 m/s²; with R + 15 m, g = 9.77046 m/s². The difference is only 0.00005 m/s² – about five parts in a million.
4. Mango and leaf, paper and coin
Q. മാവിൽ നിന്ന് മാങ്ങയും ഇലയും ഒരേ സമയം പതിക്കാൻ തുടങ്ങിയാൽ അവ ഒരുമിച്ച് താഴെ എത്തുമോ? എന്തായിരിക്കും കാരണം? – If a mango and a leaf start falling from a mango tree at the same time, will they reach the ground together? What could be the reason?
Test the idea with the textbook's activity: ഒരു കടലാസ് കഷണവും ഒരു നാണയവും ഒരേ ഉയരത്തിൽ നിന്ന് ഒരുമിച്ച് താഴോട്ട് ഇടുക. … ഇതേ കടലാസ് ചുരുട്ടിയ ശേഷം പ്രവർത്തനം ആവർത്തിക്കുക. – drop a piece of paper and a coin together; then crumple the same paper and repeat.
| Paper shape | Coin: time (s) | Paper: time (s) | Paper lands later by (s) |
|---|
Q. എന്ത് നിരീക്ഷിക്കുന്നു? … എന്ത് വ്യത്യാസമാണ് ഇപ്പോൾ നിരീക്ഷിച്ചത്? – What do you observe? What difference did you see after crumpling?
5. The feather and coin experiment (Fig 4.9)
വായു നീക്കം ചെയ്യാനുള്ള ഉപായം കണ്ടെത്തിയതോടെ ഈ നിഗമനം പരീക്ഷണങ്ങളിലൂടെ തെളിയിക്കപ്പെട്ടു. Once people could pump air out of a container, this idea was proved directly. This is the feather and coin experiment (തൂവലും നാണയവും പരീക്ഷണം).
The Moon has no air. In 1971 the Apollo 15 astronaut David Scott held a hammer and a falcon feather at the same height on the Moon and let go. Both landed together, live on television – exactly as this page predicts. (On the Moon they fall more slowly than on Earth, because the Moon's g is smaller – page 8.)
6. Calculating g for the Earth
Textbook (page 79): ഭൂമിയിലെ g യുടെ മൂല്യം കണക്കാക്കി നോക്കാം. – Calculate the value of g on the Earth. Mass of the Earth M = 6 × 1024 kg, radius R = 6.4 × 106 m.
Use g = GM/R². Multiply 6.67 × 6 in the top and 6.4 × 6.4 in the bottom; add the powers of ten in the top (−11 + 24) and double the power in the bottom ((106)² = 1012).
Jupiter has no solid surface; books quote 23 to 25 m/s² depending on the level and on its fast spin. The textbook uses 23.1 m/s². The calculator uses only g = GM/R².
- ▶️ The Apollo 15 Hammer-Feather Drop NASA
Astronaut David Scott drops a hammer and a falcon feather on the airless Moon – they land together. - ▶️ Apollo 15 Hammer-Feather Drop YouTube – NASA Solar System · 1:23
Original 1971 footage of the hammer and feather falling side by side on the Moon. - ▶️ Apollo 15 Proves Galileo Correct YouTube – NASA Video · 0:48
A quick NASA clip of the same Moon experiment, proving Galileo right. - ▶️ Brian Cox visits the world's biggest vacuum | Human Universe - BBC YouTube – BBC · 4:42
In NASA's giant vacuum chamber a bowling ball and feathers are dropped together – with no air, they fall at exactly the same rate. - ▶️ Feather and Coin in a Vacuum (A8) [1C20.10] YouTube – MIT Physics Instructional Resources Lab · 2:09
A coin and feather in a glass tube: with air the feather lags, after pumping out the air they fall together.
7. Check yourself
- The Earth's pull is an unbalanced force on a falling body, so it accelerates. This acceleration is g, the acceleration due to gravity.
- mg = GMm/R² ⇒ g = GM/R²; unit m/s². The object's mass is not in it.
- So, without air, heavy and light objects fall together (feather and coin in a vacuum tube; hammer and feather on the Moon).
- Leaves, feathers and flat paper fall slowly because of the air, not because g is smaller for them.
- For the Earth: g = 6.67 × 10−11 × 6 × 1024 ÷ (6.4 × 106)² = 9.77 ≈ 9.8 m/s².