Gravitation

Standard 9

Gravitation

Is the force pull objects towards the ground is the same that keeps the moon moving around the earth?

Newton’s hypothesis

Just pushed over the table with force F1

When you gently push the ball over the table, it drops more or less near the edge of the table covering very little horizontal distance.

Distance d1

Newton’s hypothesis

Just pushed over the table with force F1

Pushed with more force F2

If you push the ball harder (i.e. apply more force) the ball travels a longer distance horizontally before reaching the ground.

Distance d1

Distance d2

Newton’s hypothesis

If one could push the ball so hard that the earth always curves off before the ball reaches the ground then the ball would orbit earth like the moon.

Galileo’s ExperimentGalileo believed that the time taken by an object to fall to the earth is independent of its mass.

He demonstrated this by dropping two objects of different sizes and weights from the Tower of Pisa and calculating the time required by them to reach the ground.

It was found that the time taken by the objects is same. This meant that the acceleration of all the bodies because of the pull of the earth was also the same.

Since a is constant;

Galileo’s Experiment

However when we do the experiment we find that lighter objects take more time to reach the ground.

We also find a small variation in the time taken by the same object each time we do the experiment.

Why do our answers not match with what Galileo’s observations?

Mistakes made by us while noting down the time – Human errorEffect of the resistance of air to the motion of an object

Does Gravitational Force depend on distance?

Radius of earth = r km 6000000 mRadius of moon’s orbit 60r mAverage speed of moon (v) 1000 m/sAcceleration due to gravity on the surface of earth 10 m/s2

= =

= =

Factors influencing Gravitation Force

G is called the Universal Gravitation constant.G = 6.7 10-11 N m2/ kg2

Universal Law of Gravitation

Every object in the universe attracts every other object with a force that is proportional to the

product of their masses and inversely proportional to the distance between them.

Distance r

Mass = M Mass = m

𝑭=𝑮∗ 𝑴∗𝒎𝒓𝟐

Does the apple also pull the earth?

𝐹 𝑒𝑎=𝐺∗𝑀𝑒∗𝑚𝑎

𝑟2

𝐹 𝑎𝑒=𝐺∗𝑀𝑒∗𝑚𝑎

𝑟2

But the mass of the earth (6*1024 kg) is very large and hence its acceleration is extremely small and hence we don’t notice it moving

towards the apple.

Acceleration due to GravityThe acceleration produced on an object because of the gravitational force is known as acceleration due to gravity (g).

The acceleration due to gravity due to an object depends on the mass of the object and the distance from that object.

Gravity on the surface of earth

Radius of earth = r km 6400000 mMass of earth 6 * 1024 kg

Earth’s gravity with distance

In Space gravity decreases exponentially with distance

As you go deeper, gravity first increases and then decreases

Gravity on surface of JupiterRadius of Jupiter 11 times the radius of Earth.Mass of Jupiter 319 times the mass of Earth.

Mass and Weight

When you weigh something, what are you measuring?

Weight is the measure of force acting on an object.

Units of measure of weight are the same as that of force – Newton or kg m/s2.

Since mass of an object remain constant; weight of the object is directly proportional to acceleration due to gravity.

Where would you weigh moreEquator or Poles?

Earth is not a perfect sphere.

The radius of earth at the equator > radius of earth at the poles.

Since acceleration due to gravity in inversely proportional to the distance.

Earth’s gravity is therefore more at the poles and hence you will weigh more at the poles.

Free fall

Equations of motion for objects in free fall –

Since acceleration due to gravity always acts in the downward direction, g is always – 9.8 m/s2.

When an object falls only under the influence of gravity then it is said to be in free fall.

One experience weightlessness while falling freely.

APPENDIX