Final Exam Notes Physics

Final Exam Notes Physics Newtons laws: 1. An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. 2. The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. (Fnet= m x a) 3. For every action, there is an equal and opposite reaction. The Law of Action-Reaction A collision is an interaction between two objects that have made contact (usually) with each other. As in any interaction, a collision results in a force being applied to the two colliding objects. Newton's laws of motion govern such collisions. Kinematic Equations Speed is a scalar quantity that refers to "how fast an object is moving." Velocity is a vector quantity that refers to "the rate at which an object changes its position." Average Speed = 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝑻𝒓𝒂𝒗𝒆𝒍𝒆𝒅 𝑻𝒊𝒎𝒆 𝒐𝒇 𝑻𝒓𝒂𝒗𝒆𝒍 Velocity is often computed using this formula Average Velocity = 𝒑𝒐𝒔𝒊𝒕𝒊𝒐𝒏 𝒕𝒊𝒎𝒆 = 𝒅𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕 𝒕𝒊𝒎𝒆 Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity. 𝒂= △𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚 • • 𝒕𝒊𝒎𝒆 Ave. acceleration = △𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚 𝒕𝒊𝒎𝒆 = 𝒗𝒇 −𝒗𝒊 𝒕 Free-falling objects do not encounter air resistance. All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s forback-of-the-envelope calculations) The distance that a free-falling object has fallen from a position of rest is also dependent upon the time of fall. This distance can be computed by use of a formula; the distance fallen after a time of t seconds is given by the formula. Final Velocity= gravity x time. 𝒅 = 𝟎. 𝟓 ⋅ 𝒈 ⋅ 𝒕𝟐 The kinematic equations are a set of four equations that can be utilized to predict unknown information about an object's motion if other information is known. The equations can be utilized for any motion that can be described as being either a constant velocity motion (an acceleration of 0 m/s/s) or a constant acceleration motion. They can never be used over any time period during which the acceleration is changing. 𝟏 𝒅 = 𝒗𝒊 ∗ 𝒕 + 𝟐 ∗ 𝒂 ∗ 𝒕𝟐 𝒗𝟐𝒇 = 𝒗𝟐𝒊 + 𝟐 ∗ 𝒂 ∗ 𝒅 𝑽𝒇 = 𝒗𝒊 + 𝒂 ∗ 𝒕 𝒅= 𝒗𝒊 +𝒗𝒇 𝟐 ∗𝒕 Momentum/ Impulse Momentum can be defined as "mass in motion." All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion. The amount of momentum that an object has is dependent upon two variables: how much stuff is moving and how fast the stuff is moving. Momentum depends upon the variables mass and velocity. In terms of an equation, the momentum of an object is equal to the mass of the object times the velocity of the object. P= mass x velocity If both sides of the above equation are multiplied by the quantity t, a new equation results. 𝑭 ∗ 𝒕 = 𝒎 ∗△ 𝒗 The above equation is one statement of the law of momentum conservation. In a collision, the momentum change of object 1 is equal to and opposite of the momentum change of object 2. That is, the momentum lost by object 1 is equal to the momentum gained by object 2. 𝒎𝟏 ∗△ 𝒗𝟏 = −𝒎𝟐 ∗△ 𝒗𝟐 The momentum changes are equal in magnitude and opposite in direction. Work/Energy/Power When a force acts upon an object to cause a displacement of the object, it is said that work was done upon the object. There are three key ingredients to work - force, displacement, and cause. 𝑾 = 𝑭 ∗ 𝒅 ∗ 𝒄𝒐𝒔 𝚯 𝑷𝑬𝒈𝒓𝒂𝒗 =mass * g * height 𝑲𝑬 = 𝟏 ∗ 𝒎 ∗ 𝒗𝟐 𝟐 Where m = mass of object Power= 𝑾𝒐𝒓𝒌 𝒕𝒊𝒎𝒆 𝑻𝑴𝑬 = 𝑷𝑬𝒈𝒓𝒂𝒗 + 𝑷𝑬𝒔𝒑𝒓𝒊𝒏𝒈 + 𝑲𝑬 Circular Motion/Planetary Acceleration= distance/time or in this case circumference (2 𝛑 R)/time Average Speed = 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒊𝒎𝒆 = 𝟐∗𝛑∗𝑹 𝑻 Where R represents radius, T represents period The acceleration of an object moving in a circle can be determined by either two of the following equations. Acceleration = 𝒗𝟐 𝑹 Acceleration = Where v represents speed 𝟒∗𝛑𝟐 ∗𝑹 𝑻𝟐 R represents radius T represents period 𝑭𝒏𝒆𝒕 = 𝒎 ∗ 𝒂 𝑭𝒏𝒆𝒕 = 𝒎 ∗ 𝒗𝟐 𝑹 𝑭𝒏𝒆𝒕 = 𝒎 ∗ 𝟒∗𝛑𝟐 ∗𝑹 𝑻𝟐 Kepler's three laws of planetary motion can be described as follows: • • • The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses) An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas) The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. (The Law of Harmonies) 𝑭𝒈𝒓𝒂𝒗 ∞ 𝒎𝟏 ∗ 𝒎𝟐 𝒅𝟐 Projectile