GRAVITATION (physics unit:5)

Gravitational field strength tells us about the gravitational field at a place, while free-fall acceleration tells us what happens to an object when gravity is the only force acting on it.

Let's go step by step.

1. Gravitational Field Strength

First remember the definition:

Gravitational field strength at a point is the gravitational force acting on a unit mass placed at that point.

Formula:

g = Fg / m

Here:

• g = gravitational field strength

• Fg = gravitational force

• m = mass

For Earth's surface:

g = 9.8 N/kg

This can also be written as:

g = 9.8 m/s²

And this is where the confusion starts.

2. Why is g also called free-fall acceleration?

Suppose you take an object and drop it.

Imagine that there is no air resistance, and the only force acting on the object is Earth's gravitational force.

According to Newton's second law:

a = F / m

For this particular object, the force is gravitational force:

a = Fg / m

But we already defined gravitational field strength as:

g = Fg / m

Therefore:

a = g

So, when an object is freely falling under the effect of gravity alone:

Its acceleration is equal to the gravitational field strength.

Near Earth's surface:

a = g = 9.8 m/s²

h(t)=h0+v0t−12gt2h(t) = h_0 + v_0t - \frac{1}{2}gt^2

From rest at 14 m, it falls to impact.

Release height

m

Release height

Starting velocity

m/s

Starting velocity

Velocity 16.6 m/sAcceleration0 m6 m12 m18 m24 mStart

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Very simple example

You drop a ball.

Only gravity acts on it.

Therefore, the ball accelerates downward at approximately:

9.8 m/s²

That is free-fall acceleration.

3. Then why does the textbook say they are "not the same thing"?

This is the most important part.

They have the same numerical value in a particular situation, but they describe different things.

Gravitational field strength

It describes the gravitational field at a location.

It exists whether or not an object is actually falling.

Free-fall acceleration

It describes the acceleration of an object when gravity is the only force acting on it.

So:

Gravitational field strength → property of the field/location

Free-fall acceleration → motion of a freely falling object

4. Now understand the spring-scale example

This is exactly why your textbook gives that example.

Imagine you hang a 1 kg object from a spring scale.

The object is hanging at rest.

Gravity pulls it downward.

The spring pulls it upward.

These forces balance each other.

So:

Net force = 0

Therefore:

Acceleration = 0

The object is not freely falling.

But the gravitational force acting on it still exists.

For a 1 kg mass:

Fg = mg

Fg = 1 × 9.8

Fg = 9.8 N

The spring scale measures this weight/force.

So we can determine:

g = Fg / m

g = 9.8 / 1

g = 9.8 N/kg

Therefore, the scale experiment tells us about the gravitational field strength, even though the object has zero acceleration because it is being supported.

5. This is what the textbook means by "frame of reference fixed to Earth's surface"

This sounds complicated, but it isn't.

You're standing on Earth.

You hold a book in your hand.

The book is not moving.

From your point of view, the book has:

Acceleration = 0

But Earth's gravitational field is still acting on the book.

So the book experiences gravitational force downward, while your hand provides an upward force.

Therefore:

Gravitational field strength = 9.8 N/kg

but

Acceleration of the book = 0

because the book is not freely falling.

⭐ The whole concept in one table

So g can be 9.8 N/kg even when the object's acceleration is zero.