Unit 2b: Gravitational Force

As far as we know, there are four fundamental forces:

  1. Strong nuclear force
  2. Weak nuclear force
  3. Electromagnetic force
  4. Gravitational force

#1 and #2 hold atoms together. We learn about #3 later this semester.

WHAT IS GRAVITY?

  • Gravity is a force between two objects with mass
  • The two objects do not have to be in contact—all things with mass exert a gravitational force on every other thing with mass in the universe
  • An object is surrounded by a gravitational field
  • Field is a region of space that has a physical quantity (like force) at every point. The field goes out from the mass infinitely into space

THE EQUATION OF GRAVITATIONAL FORCE

  • G is the gravitational constant (don’t need to memorize).
  • It has the units m3/kgs2 (distance3/(mass * time2)
  • m1 is mass of object 1, m2 is mass of object 2
  • d is distance between them

PRACTICE:

What would be the effect of the following on the gravitational force between two objects?

  1. Doubling the mass of both objects?
  1. Increasing the distance between them 100x

CONSEQUENCES OF EQUATION:

  • Two objects apply the same gravitational forces on each other
  • As one object’s mass increases, the attractive force of gravity between them increases proportionally
  • As the distance between two objects increases, the force of gravity decreases proportionally by the square of the distance:
  • If the distance is doubled, the force is ¼ as strong
  • If the distance is tripled, the force is 1/9 as strong
  • If the distance is quadrupled, the force is 1/16 as strong
  • Therefore, gravity becomes negligible, (but still present) as both masses become very small and distances become very large.

GRAVITATIONAL FORCE ON EARTH:

  • As we are all approximately the same distance from the earth’s center of gravity, we can combine G and m2 and d2 into the number g, the gravitational strength on earth.
  • g = 9.8m/s2 so that g = acceleration (a)
  • As mass of an object on earth increases, Fgincreases, but acceleration of that object does not

ORBIT:

  • If astronauts are only a little further away from the center of gravity than we are, they should experience 90% of the force of gravity that we do. Why do they seem to be in “zero gravity”?
  • Answer: they do not, they are in free fall.
  • An object orbiting another is space is in free fall.

Tidal Forces

  • Newton’s equation treats masses as points with no volume.
  • In reality, every part of a mass has a gravitational field
  • Any object experiences a slightly larger gravitational force on the side of the object closer to the other mass (like earth).
  • If the object is large enough, the closer side of the object is noticeably closer to the other object than the further side.
  • On earth, the force between the moon and the earth is greatest on the near sides of both objects
  • Water is pulled “up” closer to the moon
  • When entering a black hole, the tidal force will pull your closer side away from your further side, ripping you apart.