MCAT Physics Equation Sheet, Schemes and Mind Maps of Physics

Download MCAT Physics Equation Sheet and more Schemes and Mind Maps Physics in PDF only on Docsity! (17411 Te ened COW Meee Leimert d= distance, t = time Ax = displacement, At = elapsed time ‘Average acceleration Av Av = change in velocity, At = elapsed time (constant acceleration a) v=vy tat otyyttdar v= 1, +2a(x—- x9) Ar Linear motion kinematics 1-D v= 2gh (Free fall fromOvelocity To apply in two dimensions, the easiest way is to choose an x-y coordinate system so that the direction of the acceleration is entirely along either the x or the y direction. This greatly simplifies things as the acceleration in the other coordinate direction will have a component of 0 and the motion in that other direction will have constant velocity. The components of motion in the x and y directions are analyzed separately. mm, G= 667x107 Navlkg Inclined Planes — mesi 6 is the angle between the inclined plane and inctine= M8 Sin @ the horizontal surface Format = M COS O Hooke’s Law The further a spring s stretched, the more force F =-kAx it pulls back with, Torque Torque, which can be roughly thought of as a t= Fl twisting force, is proportional to the force applied and the lever arm length. WORK AND ENERG Vector components v, =VvcosOs v, sin@> tand For a vector of magnitude v making an angle @ with the x-axis Work done by a constant force W = Fdcos@ Work W done by a constant force of magnitude F on an object as it is displaced by a distance d. The angle between the directions of Fanddis @. Work is positive if the object is displaced in the direction of the force and negative if it is displaced against the force. The work is zero if the displacement is perpendicular to the direction of the force. Centripetal acceleration Centripetal acceleration ag is toward the center of the circle of radius rfor an object traveling with constant speed v Kinetic energy K =4m’ Kinetic energy K for a mass m traveling ata speed v. es Gravitational potential energy U = mgh (local) u GMm r (general ) Potential energy Uis the energy that an object of mass m has by virtue of its position relative to the surface of the earth. That position is measured by the height h of the object relative to an arbitrary zero level. Newton’s first law of motion (Equilibrium) =F =0 T clockwise = T counterclockwise ‘At equilibrium, every body continues in its state of rest or of uniform speed as long as no net force and no net torque act on it. Newton's second law of motion (Dynamics) F=ma The acceleration a of an objectis directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force action the object. Conservative forces * — Gravitational force * Elastic spring force © Electric force Non-conservative forces Frictional forces Airresistance Tension Normal force Propulsion of a motor ‘Atorce is conservative if either © The work done by the force on an object moving from one point to another depends only on the initial and final positions and is independent of the particular path taken. The net work done by the force on an object moving around any closed path is zero Newton’s third law of motion Whenever one object exerts a force on a second object, the second exerts an equal and opposite force on the first. Force of static friction Fy SHFy ‘Opposes any impending relative motion between two surfaces, where the magnitude can assume any value up to a maximum of Fw where us s the coefficient of static friction and Fyis the magnitude of the normal force. Conservation of Mechanical Energy (Only holds true if non-conservative forces are ignored) ‘The total mechanical energy of a system, remains constant as the object moves, provided that the net work done by external non-conservative forces (such as friction and Force of kinetic friction Fy, = Fy Force between two surfaces sliding against one another that opposes the relative motion of the two surfaces, where sis the coefficient of kinetic friction. Force of gravity between any two objects The force Fe between two objects of masses mi; and me and separated by a distance r. The value of the universal gravitation constant is: W,,. = AK + AU + AE, E,=E, air resistance) is zero. K,+U,=K,+U, Work-energy Theorem The work due to non-conservative forces Wne is equal to the change in kinetic energy 4K plus the change in gravitational potential energy AU plus any changes in internal energy due to friction. Rest Mass Energy E=mce* The energy inherent to a particle by nature of t having a mass. P< We've helped over 50,000 students get better grades since 1999! Need help for ex itswe Check out our classroom prep sessions - customized to your exact course - at www.prep1 01.com Power Pis defined as the rate at which work is done. It can also be expressed in terms of the force F being applied to the object traveling at a speed v. It is more correct to express this version of the relationship as P= Fvcos@ where @is the angle between Fand v. MOMENTUM Linear momentum: p=mv p=mv Linear momentum pis the product of an object's mass m and velocity v. Linear momentum is a vector that points in the same direction of the velocity. Principle of conservation of linear momentum: P=P The total linear momentum of an isolated system remains constant. Impulse-momentum theorem: Ap=F +t B.-B, =F At net ‘An impulse produces a change in an object's momentum. Impulse is given by the product of average force F’ (F) and the time interval At (f) over which the force is applied. Impulse is a vector that points in the same direction as the average force. Elastic collisions: * Bodies do not stick together * Kinetic energy is conserved « Momentum is conserved Inelastic collisions: © Bodies stick together if completely inelastic ¢ Kinetic energy is not conserved « Momentum is conserved A completely inelastic collision is one in which the bodies stick together completely atter the collision. In inelastic collisions, kinetic energy is not conserved as some of the initial kinetic energy is converted into other forms of energy such as thermal and sound energy. Center of Mass (CM or CoffM) The center of mass is a point that =m,x, represents the average location for the Xm = total mass of the system. ‘oul For two bodies In a collision, the velocity of the center of me tmx mass of all the colliding objects remains a = TM, constant. on = em, FLUIDS AND SOLIDS Density Density ofa liquid at rest. Density can also be m measured relative to water, which is termed p=-2 speaific gravity. A spectic gravity > 1 means the Vv liquid is more dense than water, A specific gravity < 1 means the liquid is less dense than water Pressure The hydrostatic pressure on a fluid volume is P= (general definition) Hydrostatic pressure at a fixed depth dependent on its depth, and is equal in all directions. P= psy Buoyant Force The buoyant force on an object in fluid is upward Foon = PVE and equal to the weight of the fluid that the object displaces. Continuity Equation Q=Av The volume flow rate of a fluid Is proportional to the cross-sectional area of the pipe and the velocity of the fluid. Q,, must be equal to Qay. Bernoulli's Equation 1, P+ pay +— pv? = constat ‘One way to remember the Bernoulli equation is to think of it as an energy conservation equation. The three terms roughly correspond to pressure energy, potential energy, and kinetic energy, respectively. Elastic modulus of a solid Modulus Stress Strain ‘Ahigh modulus material is hard and rigid. Examples are metal and ceramic. A low modulus material is elastic, like rubber. Both ends fixed or free nA, a ) b=" (1=123...) One end fixed one end free nA, L=— (n=1,35,... 4 ( ) Wave Velocity The velocity of a wave Is the product of its v= fa frequency and wavelength. Wave Period 1 T=— f Sound decibels ‘Adifference of 10 in decibels corresponds to I sound intensity levels that differ by a factor of 10. B =10 log — For example, 90dB is 10 times as loud as 80dB. I, Standing Waves When a standing wave is formed on a piece of string, the string length is some fractional multiple of the standing wave wavelength. Depending on how the string is fixed, each end can be a node or an anti-node. Beat frequency Fea =|fi~ fa When two waves of constant amplitude but different frequencies interfere with each other, the resulting wave’s amplitude is confined to an envelope with some periodicity. The frequency of the envelope is the beat frequency and can be heard as distinct beats because of the amplitude variation with time. Doppler effect Af_y Maly fo ¢ Ae The apparent frequency of the source Is increased as the source approaches the observer, and is decreased as the sources leaves the observer. ELECTROSTATICS AND MAGNETISM. Bolztmann’s constant k and has a value of: k= 9.010" N-m/C* Coulomb's law (electric force) pa 22 The magnitude of the force F between two charges (Q; and Q,) in terms of the distance r between the two charges. The direction of the force is directed along the line between the two forces. This force is repulsive if the two charges are both positive or both negative, and attractive