Week 5: Gravity

Newton’s Law of Gravity

  • Newton’s Law of Gravity:

    • “Between any two masses in the universe, there is a force of attraction, called gravity, which is directly proportional to the product of the masses, and is inversely proportional to the square of the separation between the center of masses.”

      • if mass of one body increases, gravitational force between those two objects increases (and vise versa)

        • directly proportional

      • if distance between the two objects increases, the gravitational force decreases (and vise versa)

        • inversely proportional

    • Fg α\alpha mass1⋅mass2distan⁡ce2\frac{mass1\cdot mass2}{dis\tan ce^2} α\alpha m1⋅m2d2\frac{m1\cdot m2}{d^2}

      • Fg = Force of gravity

      • α\alpha = proportional to

      • G = gravity (always constant)

  • Units for force: pounds (lbs)

    • pounds = weight, how hard gravity is pulling down on you

  • mass: grams (g), kilograms (kg), milligrams (mg)

    • 1 kilogram = 1,000 grams

    • 1 gram = 1,000 miligrams

Mass vs. Weight

  • for the pictured barbell weight:

    • On Earth:

      • weight = 3lbs

      • Mass = 1.4 kg

    • In space:

      • weight = 0 lbs

      • Mass = 1.4 kg

    • On the moon:

      • weight = 0.5 lbs

      • Mass = 1.4 kg

    • Mass does not change but weight does

      • strength of gravity changes causing weight to change

  • person on top of mountain on Earth:

    • distance changes because you are farther away from center of earth

      • force of gravity decreases = weight is decreased

    • quick way to gain weight: get up higher on earth (on table, on mountain)

    • quick way to lose weight: get lower and closer to earth center

      • when actually trying to lose weight, actually trying to loose mass

Falling and “g’s”

  • Acceleration due to gravity:

    • as things are falling, gravity accelerates speed by 32 feet/ second/second or ft/ sec2

      • at two seconds, it will go at 64 ft/sec2

      • at three seconds, it will go at 96 ft/sec2

    • in metrics: 9.8 meters/second/second or m/ sec2

    • we call this “1 g” of force

      • ie: on roller coaster

      • it is possible to have more than 1g force on you

      • in an elevator that was going 1g, you would not be able to feel if elevator was moving or not

Orbits

  • moon is falling towards the Earth at 1/20th inch/second

    • also moving sideways at 2/3rd mile/second

      • causes moon to orbit the Earth

        • but misses the Earth and continues to orbit it