13.4-13.5, 13.8: Newton's Law of Universal Gravitation, Gravity and Distance: The Inverse-Square Law, & Weight and Weightlessness
Universal Gravitational Constant (G)=
6.67 x 10⁻¹¹ N⋅m²/kg² (The units are crazy to make the force come out in Newtons)
Weight reading in a moving elevator varies, but not during constant speed...what does it vary based on?
Acceleration
*Newton's Law of Universal Gravitation Equation*
*F= (Gm1m2)÷d²* Wait a minute... That's the equation we skipped over earlier, just with distance instead of radius as in the picture! ;)
Rather than rotation creating gravity, rotation creates the sense of weight by providing...
support force.
Newton did not discover gravity. Newton discovered that gravity is ________.
universal. Everything pulls on everything else in the universe in a way that involves only mass and distance.
Important things to know when dealing with Earth:
Earth's mass is 6 x 10²⁴ kg Earth's radius is 6.4 x 10⁶ m
Newton's Law of Universal Gravitation
Every object in the universe attracts every other object with a force directly proportional to the mass of each object, and inversely proportional to the distance between the centers of the objects squared
Newton's Law of Universal Gravitation Proportion:
Force of gravity~ (mass 1 x mass 2)÷ (distance)² or F~ (m1m2)÷d²
Nothing in the universe ever truly escapes from another object's gravity, no matter how...
far away it gets.
During downward acceleration, the elevator floor and scale would push less against your feet...
giving you a decreased sensation of weight and a lesser weight reading due to decompression of the scale.
During upward acceleration, the elevator floor and scale would push harder against your feet....
giving you an increased sensation of weight (equal and opposite force you exert on the scale and elevator floor) and a greater weight reading due to compression of the scale.
The condition of "weightlessness" is not the absence of gravity, but rather...
the absence of a support force.
To make the universal gravitation proportion into an equation...
the gravitational constant (G) must be added in! G describes the strength of gravity, which is the weakest of the 4 fundamental forces.
We don't think of gravity as accelerating us because...
we are in contact with the Earth.
Also by the equation, we can see that gravity decreases according to the *inverse-square law*. The force of gravity...
weakens as the square of distance
Force you exert against the supporting floor is the sensation we interpret as ______.
weight
By the equation, the force of gravity is greater when the two objects have a greater combined mass, or...
when the distance between the objects is less.
If the elevator was freely falling...
you would feel weightless