Physics 1 PDF - Basic Concepts

# Mechanics - Basic Concepts ## Velocity - Average velocity is distance traveled / time elapsed measured in m/s. - The rate of change of an object's position with respect to a frame of reference, and is a function of time - Equivalent to a specification of its speed and direction of motion - Impo...

# Mechanics - Basic Concepts ## Velocity - Average velocity is distance traveled / time elapsed measured in m/s. - The rate of change of an object's position with respect to a frame of reference, and is a function of time - Equivalent to a specification of its speed and direction of motion - Important concept in kinematics - Physical vector quantity, both magnitude and direction are needed to define it ## Acceleration - Rate of change of velocity of an object with respect to time - Object's acceleration is the net result of any and all forces acting on the object, as described by Newton's Second Law. - Sl unit for acceleration is meter per second squared (m s^-2) - Accelerations are vector quantities and add according to the parallelogram law - Calculated net force is equal to the product of the object's mass and its acceleration ## Force - Any interaction that, when unopposed, will change the motion of an object - Can cause an object with mass to change its velocity, to accelerate - Can also be described intuitively as a push or a pull - Has both magnitude and direction, making it a vector quantity - Measured in the SI unit of newton's and represented by the symbol F - F = m * a ## Impulse - Symbolized by J or Imp - The integral of a force, F, over the time interval, t, for which it acts - Impulse = Force × time = FΔt - Impulse is also a vector in the same direction as force - Impulse applied to an object produces an equivalent vector change in its linear momentum, also in the same direction ## Work - Work = Force ⋅ Distance - W = F ⋅ d - A force is said to do work if there is a displacement of the point of application in the direction of the force - For example, when a ball is held above the ground and then dropped, the work done on the ball as it falls is equal to the weight of the ball (a force) multiplied by the distance to the ground (a displacement) - Work transfers energy from one place to another or one form to another - Sl unit of work is the joule (J) ## Energy - Energy is the property that must be transferred to an object in order to perform work on or to heat - the object, and can be converted in form, but not created or destroyed. - Sl unit of energy is joule (J) - Common energy forms include the kinetic energy of a moving object, the potential energy stored by an object's position in a force field (gravitational, electric or magnetic), the elastic energy stored by stretching solid objects, the chemical energy released when a fuel burns, the radiant energy carried by light, and the thermal energy due to an object's temperature. - Mass and energy are closely related - Due to mass-energy equivalence, any object that has mass when stationary in a frame of reference also has an equivalent amount of energy whose form is called rest energy ## Power - Rate of doing work, amount of energy consumed per unit time - It has no direction and is a scalar quantity - Unit of power is the joule per second (J/s). - Another common and traditional measure is horsepower - Integral of power over time defines the work performed - Power requires both a change in the physical universe and a specified time in which the change occurs **P = W/t** Where: * **P** = Power * **W** = Work done * **t** = Time taken ## Energy Conservation Law - Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed - Equivalent to mass, and this mass is always associated with it - Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence - The Formula E = mc² quantifies the relationship between rest-mass and rest-energy within the concept of special relativity - Part of the rest energy (equivalent to rest mass) of matter may be converted to other forms of energy (still exhibiting mass), but neither energy nor mass can be destroyed; rather, both remain constant during any process ## Momentum Conservation Law - In a closed system the total momentum is constant. - Suppose, for example, that two particles interact. Because of the third law, the forces between them are equal and opposite. If the particles are numbered 1 and 2, the second law states that F₁ = dp₁/dt and F₂ = dp₂/dt. - This law holds no matter how complicated the force is between particles. - Similarly, if there are several particles, the momentum exchanged between each pair of particles adds up to zero, so the total change in momentum is zero. - This conservation law applies to all interactions, including collisions and separations caused by explosive forces. ## Momentum - Linear momentum, translational momentum, or simply momentum - Sl unit kg ⋅ m/s - Product of the mass and velocity of an object, quantified in kilogram-meters per second - Dimensionally equivalent to impulse, the product of force and time, quantified in newton-seconds - Newton's second law of motion states that the change in linear momentum of a body is equal to the net impulse acting on it - Linear momentum is a vector quantity, possessing the same direction as the velocity ## Uniform and Accelerated Motions - Uniform or constant acceleration is a type of motion in which the velocity of an object changes by an equal amount in every equal time period - Uniform acceleration is e.g. an object in free fall in a uniform gravitational field - The acceleration of a falling body in the absence of resistances to motion is dependent only on the gravitational field strength g - By Newton's Second Law the force, F, acting on a body **m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂** Where: * **m₁** = Mass of the 1^st object * **m₂** = Mass of the 2^nd object * **u₁** = Initial velocity of the 1^st object * **u₂** = Initial velocity of the 2^nd object * **v₁** = Final velocity of the 1^st object * **v₂** = Final velocity of the 2^nd object ## Newton's Laws **First Law:** - Defines the force qualitatively - In an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force **Second Law:** - Offers a quantitative measure of the force - In an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma. **Third Law:** - Asserts that a single isolated force doesn't exist - When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body. **Equations** **Velocity:** * v = u + at * s = ut + 1/2 at² * s = 1/2 (u + v)t * v² = u² + 2as Where: * **a** = acceleration * **v** = final velocity * **u** = initial velocity * **t** = time taken * **s** = displacement