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By: ChasingStars#
AP Physics 1
Based on College Physics For e Ap Physics 1 Course
Source: Pexels Unit 3: Circular Motion & Gravitation Expectations (Based on College Boardโs Objectives) - โ Students understand that objects and systems have properties and may have internal structure. โ Students can calculate gravitational force on an object in a gravitational field to demonstrate their understanding that there are fields existing in space that can be used to explain objectsโ interactions. โ Students can approximate a numerical value of the gravitational field ( g ) near the surface of an object from its radius and mass relative to those of the Earth or other reference objects. โ Students can describe a force as an interaction between two objects and identify both objects for any given force by using free body diagrams and the possible application of Newtonโs Third Law of Motion. โ Students can use Newtonโs law of gravitation to calculate the gravitational force between two objects and use that force in contexts involving orbital motion. โ Students can evaluate, using given data, whether all the forces on a system or whether all the parts of a system have been identified.
Module 1: Universal Gravitation
Gravitation is the universal attraction force acting between all matter
โ Gravitational forces can be found between any two bodies in the universe โ Any object that has mass exerts a gravitational force on another object โ Gravity is due to the mass of Earth โ Symbol: ๐น (^) ๐บ โ Proportional to the objectsโ masses ( ๐ 1 and ๐ 2 ) and inversely proportional to the distance ( )๐ between the objects squared such that: ๐น ๐บ ฮฑ ๐ 1 ๐ (^2) ๐^2 โ The relationship doesn't give the exact value of the gravitational force between the objects without the addition of the Universal Gravitational Constant โ A constant with the magnitude of 6. 67 * 10 โ โ SI Unit: [Nm^2 / kg^2 ] or [m^3 / (kg * s)^2 ] โ Symbol: ๐บ โ The universal force of gravitation between any two objects with mass in the universe is then found by the equation: ๐น ๐บ
๐ 1 ๐ (^2) ๐^2 โ Gravitational force will always be directed toward the other object such that the two forces constitute a Newtonโs Third Action-Reaction pair
Module 3: Applications of Circular Motion and Gravitation
There are many applications of these concepts in real life:
Highway/road banking is the occurrence of edges being
raised at an angled for curved roads to allow vehicles to
make safe turns with less reliance on friction
โ When a car goes around a curve, there is a net force towards the center of the circle that contains the curve as an arc; if the road is flat, that force is supplied by friction between the tires and the pavement. โ If the wheels and tires of the car are rolling normally (without slipping or sliding), the bottom of the tire is at rest against the road at each instant, therefore, the friction is static โ With insufficient frictional force, the car will tend to move more nearly in a straight line, and begin to skids/slides (friction becomes kinetic friction) โ For a given banking angle, there will be one speed for which no friction at all is required, which occurs when the component of the normal force towards the center of the curve is equal to the centripetal force. [Derived equation for special angle ฮธ = ๐๐๐๐ก๐๐(๐ฃ )] 2 /๐๐)
Orbital motion refers to the three special laws called Keplerโs Laws of Planetary Motion
โ Keplerโs 1st Law states that the planetโs path about the Sun is an ellipse with the Sun at one focus โ Ellipse โflatnessโ is measured in eccentricity, running from a perfect circle of 0 to 1 โ Keplerโs 2nd Law states that each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal periods of time โ More planetary distance is covered when the planet is at Perihelion (position closer to Sun) because the planet is moving faster here โ The speed of the orbiting body and its distance from the object that it is orbiting around ( )๐ relates through the equation ๐ฃ = ๐บ๐ (^) ๐/๐
โ Keplerโs 3rd Law states that the ratio of the squares of the periods of any two planets revolving around the Sun is equal to the ratio of the cubes of their semi-major axes โ Semi-major axis is equal to half the major-axis of the orbit and represents the planets mean distance from the Sun โ This only applies to objects orbiting the same attracting center like the Sun โ The mathematical expression was of ( , where indicates planet 1, ๐ (^) ๐ ๐ (^) ๐2^ ) 2 = ( ๐ (^) ๐ ๐ (^) ๐2^ ) 3 ๐ 1
2 indicates planet 2, and ๐represents the radius โ Satellites are a smaller scale of orbiting motion โ They experienced centripetal acceleration (provided by the force of gravity)
Conical pendulum comprises of a mass attached to a string that is
held at the opposite end and swing so that the mass moves at a
constant speed in a circle (string would create a cone shape)
โ The pendulum experiences centripetal acceleration due to a component of the tension force
Weightlessness refers to the phenomenon where objects can experience an โ apparent weight โ
such that they feel lighter or heavier than they really are
โ Apparent weight will depend on the direction of acceleration and whether other forces acting on the object are greater or less than the weight force โ Occurs when objects are in reference frames where ๐ = ๐(like astronauts) โ To experience real weightlessness, the object would have to be extremely far away from any object with mass, making the gravitational force really small
