Gravity

Don’t let it drag you down…..

During the Great Plague of 1665, Isaac Newton was home from college and began thinking about gravity. A century before him, Johannes Kepler developed laws to explain the motions of the planets. Newton wondered if the same force caused an apple to fall to the ground from a tree.

This led him to the Law of Universal Gravitation:

Between every two objects there exists a force of attraction. This force is proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

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r

mGmF

* No problems will use this formula

In equation form:

The region around a mass in which a second mass will experience a gravitational force is described as a gravitational field.

The strength of the field at any place is defined as the gravitational force a unit mass (1 kg) would experience, if placed there.

This strength is represented by a 'g'. When a gravitational field is drawn, the field lines are closer together where it is strong. Where it is weaker, they are further apart.

This diagram implies that gravity is weaker as you climb in altitude.

A graph of gravity at different altitudes would appear somewhat like this.

al t i tude

gravi ty

1 0 N /kg

4 0 0 km

9 .5 N /kgNotice that at an altitude of 400 km gravity still pulls at about 9.5 N/kg. Aren't space shuttle astronauts experiencing weightlessness“ ?

The space shuttle astronauts (and anything else in orbit) are actually falling forever. They just never land. Why? The shuttle is travelling at a great horizontal speed. Add the vectors graphically

E ar thE ar th

The vector sum of the horizontal motion and gravity causes the shuttle to orbit the Earth at high speed. Since gravity is constantly pulling down on the astronauts, they are in constant free fall, which is apparent weightlessness. The actually do have a weight (Fw = mg) , we just can't measure it.

An object's weight is simply a measure of the force of gravity on the object at that particular instant. Since weight is a force, and gravity is an acceleration, therefore:

 

Fw = mg

where Fw = weight, m=mass, g=gravitational field strength

 

The greater the mass, the greater the weight, since g remains constant.

Weight

For example, when you stand on a bathroom scale, the scale reads the amount of force you are exerting on it due to gravity and converts it to mass units (kg).

But, remember Newton's Law that says that there is an equal and opposite reaction force. The scale exerts an upward force on you. This upward force is known as the normal force. It always opposes gravity.

Now, suppose you took that scale onto an accelerating elevator. You ride the elevator while standing on the scale. Since the elevator (and thus the scale) are accelerating you up in the air, it must be applying a greater normal force on you. Since you must react with an equal and opposite force (to keep Newton happy) you appear to weigh MORE because the scale does not know the difference between riding in an elevator and a person with a greater gravitational pull.

animation

And if you were to ride that elevator down, you would be pushing less on the scale and thus weigh LESS.