Physics Equations

Front 1

If 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, then is the force conservative or non-conservative?

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conservative

Front 2

Conservative or non-conservative?: gravitational force

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conservative

Front 3

If the net work done by a force on an object moving around any closed path is greater than zero, then is the force conservative on non-conservative?

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non-conservative

Front 4

Conservative or non-conservative?: frictional force

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non-conservative

Front 5

Conservative or non-conservative?: normal force

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non-conservative

Front 6

Conservative or non-conservative?: elastic spring force

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conservative

Front 7

Conservative or non-conservative?: air resistance

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non-conservative

Front 8

Conservative or non-conservative?: tension

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non-conservative

Front 9

Conservative or non-conservative?: electric force

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conservative

Front 10

Conservative or non-conservative?: propulsion of a motor

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non-conservative

Front 11

Bodies stick together; elastic, inelastic or completely inelastic?

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completely inelastic

Front 12

T-F: momentum is conserved in elastic collisions, but not in inelastic collisions

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false; momentum is conserved in elastic, inelastic and completely inelastic collisions

Front 13

What type of collision?: kinetic energy is not conserved (some of the initial kinetic energy is converted to other forms of energy such as thermal or sound energy)

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inelastic collision (vice a "completely inelastic collision")

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What type of collision?: the bodies stick together completely after the collision

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completely inelastic collision

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What type of collision?: bodies do not stick together

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elastic collision

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What type of collision?: kinetic energy is conserved

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elastic collision

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What type of collision?: momentum is conserved

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elastic, inelastic, completely inelastic collisions

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T-F: The elastic modulus of a solid is stress divided by strain

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TRUE

Front 19

Is a hard and rigid material like metal or ceramic high modulus or low modulus?

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high modulus

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Is an elastic material like rubber high modulus or low modulus?

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low modulus

Front 21

A difference of 10 in decibels corresponds to a factor sound intensity difference of 10, or 100?

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10

Front 22

Average speed; d is distance and t is time.

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Front 23

Average velocity; Δx is displacement and Δt is elapsed time

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Average acceleration; Δv is change in velocity and Δt is elapsed time

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Linear motion kinematics 1-D (with constant acceleration a); 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 zero component (constant velocity). The components of motion in the x and y directions are analyzed separately.

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Vector components; for a vector of magnitude x making an angle θ with the x axis

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Front 27

Centripetal acceleration; a-sub-r is toward the center of the circle of radius R for an object traveling with constant speed v.

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Newton's 1st Law (Equilibrium); 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.

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Newton's 2d Law; The acceleration a of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of acceleration is in the direction of the net force acting on the object.

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Force of static friction; Opposes any impending relative motion between two surfaces, where the magnitude can assume any value up to a maximum of μ<sub s>F<sub N> where μ<sub s> is the coefficient of static friction and F<sub N> is the magnitude of the normal force.

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Front 31

Force of kinetic friction; Force between two surfaces sliding against one another that opposes the relative motion of the two surfaces, where μ<sub k> is the coefficient of kinetic friction.

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Front 32

Force of gravity between any two objects; The force F<sub G> between two objects of masses m<sub 1> and m<sub 2> and separated by a distance r. The value of the universal gravitational constant G is 6.67 x 10<-11> Nm<2>/kg<2>

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Inclined Planes; θ is the angle between the inclined plane and the horizontal surface

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Front 34

Hooke's Law; The further a spring is stretched, the more force it pulls back with.

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Front 35

Torque; Torque, which can be roughly thought of as a twisting force, is proportional to the force applied and the lever arm length.

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Front 36

Work done by a constant force; 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 F and d is θ. 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.

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Kinetic energy K for a mass m traveling at velocity v

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Front 38

Gravitational potential energy; potential energy U is 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 height h of the object relative to an arbitrary zero level.

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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 air resistance) is zero.

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Work energy theorem; the work due to non-conservative forces W<sub nc> is equal to the change in kinetic energy delta K plus the change in gravitational potential energy delta U plus any changes in internal energy due to friction.

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Rest mass energy; the energy inherent to a particle by nature of it having a mass;

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Front 42

Power P is 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 = Fvcosθ where θ is the angle between F and v

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Linear momentum p is the product of an object's mass m and velocity v. Linear momentum is a vector that points in the same direction as velocity.

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Principle of conservation of linear momentum; the total linear momentum of an isolated system remains constant.

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Impulse-momentum theorem; an impulse produces a change in an object's momentum. Impulse is given by the product of average force and the time interval over which the force is applied. Impulse is a vector that points in the same direction as the average force.

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Center of Mass for one body; a point that represents the average location for the total mass of the system. In a collision, the velocity of the center of mass of all the colliding objects remains constant.

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Front 47

Center of Mass for two bodies; a point that represents the average location for the total mass of the system. In a collision, the velocity of the center of mass of all the colliding objects remains constant.

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Front 48

Density; density of a liquid at rest. Density can also be measured relative to water, which is termed specific gravity. A specific gravity greater than 1 means the liquid is more dense than water. A specific gravity less than 1 means the liquid is less dense than water.

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Pressure (general definition); hydrostatic pressure at a fixed depth; the hydrostatic pressure on a fluid volume is dependent on its depth, and is equal in all directions.

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Hydrostatic pressure at a fixed depth; the hydrostatic pressure on a fluid volume is dependent on its depth, and is equal in all directions.

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Front 51

Buoyant force; the buoyant force on an object is upward and equal to the weight of the fluid that the object displaces

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Front 52

Continuity equation; the volume flow rate of a fluid is proportional to the cross-sectional area of the pipe and the velocity of the fluid. Q<sub in> must be equal to Q<sub out>

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Bernoulli's Equation; 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

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Wave Velocity; the velocity of a wave is the product of its frequency and wavelength

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Wave period; the period of a wave is inversely proportional to its frequency

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Sound decibels

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Standing waves; both ends fixed or free; 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

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Standing waves; one end fixed and one end free; 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

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Beat frequency; 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.

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Doppler effect; the apparent frequency of the source is increased as the source approaches the observer, and is decreased as the source leaves the observer.

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Front 61

Coulomb's law (electric force); k = 9 x 10<9> Nm/C<2> is the Boltzmann constant; the magnitude of the force F between two charges (Q<sub 1> and Q<sub 2> 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 if one charge is positive and the other negative

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Electric field due to a point charge q at a distance r; E is a vector and points away from a positive charge and toward a negative charge

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Electric potential energy; the potential energy stored between the interaction between two point charges

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Electric potential; the electric potential V due to a point charge q at a distance r away from the charge

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Constant electric field equations; note that the force F is in the same direction as the electric field E if the charge q is positive and in the opposite direction if the charge is negative; the energy gained by some charge in a field is simply force times the distance traveled. Potential is the energy per unit charge.

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Force on a charge moving in a magnetic field; a charge q moving in a magnetic field B (a vector) with velocity v (a vector) experiences a force F (a vector). The magnitude of this force can also be expressed in terms of the angle θ between v (a vector) and B (a vector).

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Ohm's law; the potential difference V across a device is given by its resistance R and the current I that flows through it

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Resistance of a wire; the resistance R of a length L of wire with a cross-sectional area A and resistivity ρ. Resistivity has units Ωm

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Electric power; with help from Ohm's law, electric power P can be calculated using any combination of two of the following quantities: resistance R, voltage V or current I

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RMS voltage and current (AC circuits); the root-mean-square values can be calculated from the peak values (V<sub 0> and I<sub 0> and are used to calculate the average power P<bar> in AC circuits.

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Average power P<bar> in AC circuits, the root-mean-square values for V<sub rms> and I<sub rms> can be calculated from the peak values (V<sub 0> and I<sub 0> and are used to calculate P<bar>

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Resistance in series

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Resistances in parallel

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Capacitance; a higher capacitance capacitor can store more charge at the same voltage

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Capacitors in series and parallel

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Electric energy stored by a capacitor; amount of electric energy stored in a capacitor is given in terms of the capacitance C and the potential difference between the conductors V.

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Snell's law; the angle of incidence θ<sub 1> is with respect to the perpendicular of the surface between the two media (with indices of refraction n<sub 1> and n<sub 2>). The angle of refraction θ<sub 2> is also with respect to the perpendicular.

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Total internal reflection; the critical angle θ<sub c> is the angle of incidence beyond which total internal reflection occurs. The index of refraction for the medium in which the incident ray is traveling is n<sub 1>

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Energy of one photon; the energy of light is dependent on its frequency; H is the Planck constant 6.63 x 10<-34> m<2>kg/s

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Index of refraction; the higher the index of refraction is for a medium, the slower is the speed of light in that medium.

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The lens equation; the focal length of the lens f is: positive for converging lens, negative for diverging lens; the object distance d<sub o> is positive if it is on the side of the lens from which the light is coming, negative if on the opposite side; the image distance d<sub i> is positive if it is on the opposite side of the lens from which the light is coming and negative if on the same side.

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Lateral magnification; for an upright image, the magnification m is positive and for an inverted image m is negative.

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Power of a lens

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Focal length of a spherical mirror; for a spherical mirror, the focal length is half of the radius of curvature

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