Physics and Mathematics
Weightlessness
1. Concept Overview
Weightlessness is the condition in which a body experiences no apparent weight — that is, the normal reaction (or contact force) on it becomes zero.
Although the gravitational force still acts, the body and its surroundings accelerate equally under gravity, creating the sensation of being weightless.
A common example is an astronaut in an orbiting satellite — both the astronaut and the satellite are in free fall around the Earth, hence experiencing weightlessness.
2. Explanation and Derivation
Let:
- Mass of body = [m]
- Acceleration due to gravity = [g]
- Actual weight = [W = m g]
- Apparent weight = [R] (normal reaction)
Case 1: Body at rest on the surface
Weight is balanced by the normal reaction:
[
R = m g
]
Case 2: Body in a freely falling lift
If the lift falls freely under gravity, acceleration [a = g].
The apparent weight becomes:
[R = m (g – a)] [= m (g – g) = 0]
Thus, the person feels weightless.
Case 3: Body in an orbiting satellite
In an orbit, both the satellite and astronaut are acted upon by the same gravitational acceleration ([a = g’]).
Since there’s no contact force acting between them,
[
R = 0
]
Hence, both experience weightlessness.
3. Dimensions and Units
| Quantity | Symbol | Dimensions | SI Unit |
|---|---|---|---|
| Weight | [W] | [M L T⁻²] | [N] |
| Gravitational acceleration | [g] | [L T⁻²] | [m/s²] |
| Normal reaction | [R] | [M L T⁻²] | [N] |
4. Key Features
- Weightlessness does not mean absence of gravity.
- It occurs when the normal reaction becomes zero.
- Experienced during free fall, orbiting motion, or inside a spacecraft.
- Astronauts appear to “float” because they and their surroundings accelerate equally under gravity.
- Artificial weightlessness can be created in aircrafts (parabolic flight).
- The body still has mass and inertia, even if it feels weightless.
5. Important Formulas to Remember
| Formula | Description |
|---|---|
| [W = m g] | True weight of the body |
| [R = m (g – a)] | Apparent weight when accelerated upward/downward |
| [R = 0] | Condition for weightlessness |
| [R = m (g – g’)] | In orbit, effective weightlessness condition |
| [a = g] | Condition for free fall |
6. Conceptual Questions with Solutions
1. What is meant by weightlessness?
It is the condition in which a body experiences zero apparent weight, i.e., normal reaction [R = 0].
2. Does weightlessness mean there is no gravity?
No. Gravitational force still acts; both body and surroundings accelerate together under it.
3. Why do astronauts in a satellite feel weightless?
Because both they and the satellite are in free fall around Earth, so no normal reaction acts on them.
4. What happens to the apparent weight in a freely falling lift?
Apparent weight becomes zero since [R = m(g – a) = 0].
5. Is true weight zero during weightlessness?
No, true weight ([m g]) still exists; only apparent weight is zero.
6. Can weightlessness occur on Earth?
Yes, during free fall, like in parabolic flight or falling elevator.
7. Why does an astronaut float in a spaceship?
Because the spaceship and astronaut both accelerate equally under gravity.
8. What causes apparent weight?
The normal reaction force provided by the surface on which the body rests.
9. Why is there no weightlessness on Earth’s surface?
Because the ground provides an upward normal reaction equal to the body’s weight.
10. What is the condition for weightlessness?
When [R = 0] or [a = g].
11. Can a person experience partial weightlessness?
Yes, when acceleration [a < g], apparent weight decreases but not zero.
12. How is weightlessness simulated on Earth?
By flying aircrafts in a parabolic trajectory creating short intervals of free fall.
13. Is mass affected during weightlessness?
No, mass remains constant; only apparent weight changes.
14. What happens to a spring balance reading in a freely falling lift?
It reads zero because tension (apparent weight) vanishes.
15. Why is it called “zero gravity” in space?
It’s a misnomer — gravity still acts; objects are in continuous free fall.
7. FAQ / Common Misconceptions
1. Weightlessness means zero gravity.
❌ False. Gravity exists; only contact force is zero.
2. Astronauts are beyond the reach of gravity.
❌ False. They are under Earth’s gravity but in continuous free fall.
3. Weightlessness means loss of mass.
❌ False. Mass remains unchanged.
4. Weightlessness can occur only in space.
❌ False. It can occur during free fall on Earth too.
5. In orbit, gravity is zero.
❌ False. Gravity provides the centripetal force for orbital motion.
6. Weightlessness is permanent in space.
❌ False. It exists only while in free fall or orbit; not if thrust is applied.
7. Objects in orbit float due to lack of air.
❌ False. They float due to free fall, not absence of air.
8. Apparent weight can never be zero.
❌ False. It becomes zero in free fall or orbiting condition.
9. A satellite in space has no gravitational potential energy.
❌ False. It has negative gravitational potential energy due to Earth’s pull.
10. Weightlessness removes gravitational attraction.
❌ False. Gravitational attraction remains; only support reaction vanishes.
8. Practice Questions (With Step-by-Step Solutions)
Q1. Explain why astronauts feel weightless in a satellite orbiting the Earth.
Solution:
Both astronaut and satellite are in free fall under Earth’s gravity, experiencing the same acceleration. Hence, no contact force acts between them, and apparent weight becomes zero.
Q2. What is the apparent weight of a body of mass [50 kg] in a lift falling freely under gravity?
Solution:
[R = m (g – a)] [= 50 (9.8 – 9.8) = 0]
Hence, the body feels weightless.
Q3. A body in a lift moving downward with acceleration [a = 3 \text{ m/s}^2]. Find its apparent weight if [m = 70 kg].
Solution:
[R = m (g – a)] [= 70 (9.8 – 3)] [= 476 \text{ N}]
Apparent weight = 476 N (less than true weight).
Q4. When will a man of mass [m] in a lift experience weightlessness?
Solution:
When the lift’s acceleration [a = g],
[
R = m(g – g) = 0
]
Condition for weightlessness.
Q5. A 60 kg astronaut experiences weightlessness in orbit. Calculate the gravitational force acting on him.
Solution:
True weight = [m g’]
At an orbital height where [g’ = 8.7 \text{ m/s}^2]:
[
W = 60 × 8.7 = 522 \text{ N}
]
Though gravitational force acts, apparent weight = 0 due to free fall.
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