2.25 Gravity

Understanding Gravity

Newton discovered the Law of Universal Gravitation prior to discovering the Laws of Motion. The *Law of Universal Gravitation* tells us that every object in the universe is attracted to one another by a force. How much they are attracted to each other depends on the object's mass and the distance between them. Einstein's Theory of General Relativity added a new perspective on gravity by introducing the concept of a four-dimensional universe. He theorized that the mass of an object distorts space time. Although Einstein's description of gravity is very different from Newton's, they both describe the weak gravitational forces in the same way. However, Einstein's theory does a more accurate job of describing strong gravitational forces. Both Newton and Einstein have contributed to our understanding of gravitational force.

Galileo's discoveries regarding falling objects

Galileo discovered that objects pick up speed at the same rate, regardless of weight when *gravity is the only force* acting on the objects. Two objects of different mass will land at the same time. If you drop a crumbled paper and a flat sheet of paper, the crumpled paper will land first because there is less surface area for the air to hit against it. The flat paper will float to the ground because it is slowed down by the air around it. Air resists the flow of objects.

The difference between mass and weight

Mass: the amount of matter in an object. The greater the mass of an object, the more difficult it is to slow down, speed up, or change direction of the object's motion. Weight: a measure of gravitational attraction of an object.

Newton's discoveries regarding gravity

Newton stated that gravity depends on the mass of the objects and their distance from each other. The force of gravity follows an *inverse squared* relationship. This relationship explains that the intensity of the force of gravity is inversely proportional to the square of the distance of the two objects. Many intensities fall off according to the inverse squared relationship. Action...Inverse...Squared...Intensity: *Double* the distance...*2* becomes 1/2...(1/2)^2 = 1/4...1/4 times as strong *Triple the distance*...*3* becomes 1/3...(1/3)^2 = 1/9...1/9 times as strong A *quarter* the distance...*1/4* becomes 4...(4)^2 = 16...16 times as strong

Gravity and Weight

On Earth, gravity is what gives us weight. A scale measures the amount of force your mass exerts on the Earth because of gravity. The combination of your mass and the gravitational force results in your weight on Earth. The Moon is much smaller than the Earth and has less mass, giving it a weaker gravitational force. This weaker force means that if you were to stand on a scale on the Moon, your weight would only be one sixth what it is here on Earth. Your mass did not change, but the Moon's weaker gravitational force pulls you down on the scale with less force than the gravity on Earth.

Gravity

*Gravity* is a force of attraction between two objects that depends on two things: mass and distance. *Mass*: The greater the mass of two objects, the greater the gravitational force between the objects. Humans do not feel the Sun's gravity pulling on them, but the Sun's strong gravitational force keeps the Earth in its orbit! Because the Earth has a much greater mass than a human being, it feels a stronger gravitational force from the Sun than we do. *Distance*: The greater the distance between the objects, the weaker the gravitational force between them. The strength of a gravitational force decreases with an increase in distance. We know that the Sun has a stronger gravitational force than the Earth because it has a lot more mass than the Earth. However, because we are so much closer to the Earth, its gravity has a stronger affect on us than does the Sun's gravity. Although, gravity is the weakest of the four fundamental forces, it has a large range and can be experienced over a long distance. Gravity is the force of attraction that pulls objects toward the center of the Earth and that holds the moon in orbit around the Earth. Greater masses attract with more gravitational force, and the force weakens as the objects get farther apart.

Gravity and free fall motion

Gravity is an attractive force that acts on any two objects with mass. Normally, when we think about gravity, we think about the Earth's gravitational pull on all objects. Any two objects exert a gravitational force on each other; however, you need a huge mass, such as that of a planet, to really cause objects to move based on mass alone. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. There are two important motion characteristics that are true of free falling objects: -Free falling objects do not encounter air resistance. -All free falling objects on Earth accelerate *downward* at a rate of 9.8 m/s^2 (sometimes just 10 m/s^2 is used for simplicity). The second bullet is important to note because when you throw an object upward, it has a positive vertical velocity. Because of the downward (negative) acceleration, the object slows down until it reaches a velocity of zero. This is when it is at its highest point. Is the acceleration also zero? No. The object continues to have that downward acceleration, and as the object falls, its velocity is now negative and so is its acceleration. This causes the object to speed up as it falls.

Falling for Gravity

There is one more factor that comes into play. On Earth, we have a force called air resistance that can slow down the speed of falling objects. *Air resistance* is caused by the friction between a falling object and the particles in air. The amount of air resistance a falling object experiences is based on the shape of the object and the speed at which it falls. *All objects, regardless of their mass, experience the same acceleration when in a state of free fall*. When the only force is gravity, and there is no air resistance, the acceleration is the same value for all objects. In order to remove air resistance, we would need to drop the objects without the presence of air. Scientists can use a container called a vacuum, a chamber from which nearly all air has been removed, to remove the friction caused by air resistance.