Equations (by definition) Flashcards by Mark Rooke

Write out all three equations that use acceleration, velocity, and time.

v_f = v_i + at

(1/2)at²+ v_it + ∆x

v_f² = v_i²+ 2a(∆x)

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What is the equation for the measurement of the gravitational force between two objects?

F = (Gm₁m₂) / r²

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What equation measures torque?

And what are its units?

T = rFsinθ

Torque is unitless

r is the radius of the arm
F is the force
θ is the angle of force applied

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What is the equation for rotational motion?

F = (mv²) / r

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What is the general equation for power?

P = (W / t)

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What is the general equation for work?

W = F d cos θ

F is the force applied
d is the displacement of the object
θ is the angle between the applied force and the displacement vector

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What is the total mechanical energy equation?

E = U + K

U = potential energy

K = kinetic energy

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What’s the equation for momentum?

p = mv

where m is mass and v is velocity

DO NOT confuse momentum and power

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What are the three equations representing impulse?

I = F∆t
(where F is force and T is time)

I = ∆p
(where p is a change in momentum, not power)

I = mv_f - mv_i

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What does it mean in a collision if “momentum is conserved” ?

It means that the momentum before the collision is the same as the momentum after the collision

p_ai + p_bi = p_af + p_{bf<br></br><br></br>This is sometimes called an “elastic collision”}

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What is a completely elastic collision?

A collision where total kinetic energy and total momentum are conserved (there was no energy lost to heat, light, or deformation), like two objects perfectly boucing off each other

(1/2)m_av_ai² + (1/2)m_bv_bi² = (1/2)m_av_af² + (1/2)m_bv_bf²

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What is an inelastic collision?

Do not confuse this with “comlpetely inelastic”

When two objects collide and move away from each other, and sound/light/heat/energy is released.

(1/2)m_av_ai² + (1/2)m_bv_bi² > (1/2)m_av_af² + (1/2)m_bv_bf²

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What is a completely inelastic collision, and what’s the best equation to represent it?

When two objects collide and stick to each other, rather than moving apart. Total kinetic energy is not conserved.

m_av_ai + m_bv_bi = (m_a + m_b) v_f

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What is mechanical advantage? What equation can be used to represent it?

Mechanical advantage = (force in / force out)

It’s the ratio of the force exerted on an object by a simple machine to the force actually applied on the machine

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What’s the conversion factor of Celsius to Kelvin?

K = C + 273

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What’s the equation for the measurement of thermal expansion?

∆L = aL∆T

∆L is the change in length
L is the original length
∆T is the change in temperature
a is the expansion constant

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What is the equation for thermal volume expansion?

∆V = BV∆T

Where ∆V is the change in volume
V is the original volume
∆T is the change in temperature
B is the volume constant (this is 3a if given the length constant)

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What is the equation for specific heat?

Q = mc∆T = mc(T_f - T_i)

Where c is the specific heat
Q is in joules

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A reaction is said to be isovolumetric.

What does that mean?

Isovolumetric means that it was held at a constant volume
∆U = Q

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A reaction is said to be adiabatic.

What does that mean?

The reaction had no heat exchange.

∆U = -W

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A reaction is said to be in a closed cycle.

What does that mean?

Also called isothermal, it means that the temperature of the reaction stays constant.

Q = W

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What is an equation for measuring entropy?

∆S = Q / T

Q is heat gained or lost

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What is specific gravity?

What’s an equation to find it if given the density of an object?

Specific gravity is a density ratio. It has no units.

If given the density of an object:

specific gravity = (density of object / density of water)

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What’s the equation for pressure?

What is the SI unit?

pressure = (force / area)

SI unit is Pascal

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What is absolute pressure? What is the equation for absolute pressure?

Absolute pressure is the total pressure exerted on an object that's submerged in fluid. P = P_o + *p*gh P is the absolute pressure Po is the pressure at the surface of the fluid *p* is the density of the fluid, gh is gravity x height

What is gauge pressure? What's an equation to calculate gauge pressure?

Gauge pressure is the measurement of the pressure in an enclosed space that is above normal atmospheric pressure P_g = P - P_atm

What is Pascal's Principle? What are two equations associated with it?

When a change of pressure is applied to an enclosed fluid, the pressure change will be transmitted undiminished through all parts of the fluid and the containing walls of the vessel. P = (F₁ / A₁) = (F₂ / A₂) F₂ = F₁ (A₂ / A₁)

What is the equation for buoyant force?

F_buoyant = (V_displaced fluid)(p_fluid)g Where *p* is density and g is gravity

A liquid is flowing through a pipe with openings of different size. What equation can find the fluid's velocity?

This is the continuity equation v₁A₁ = v₂A_{2

Fluids flow faster through smaller cross sectional areas}

What is Coloumb's Law? What is its equation?

It gives the magnitude of electrostatic force between two charges: F = k ( (q₁q₂) / r²) Where k is the permitivity of free space constant

What equation measures the electrostatic force between two charges?

Coulomb's Law: F = k ((q₁q₂) / r²)

What are two equations for determining the magnitude of an electric field?

E = F / q_o E = kq / r^{2

Where q_o is the test charged placed in the field and F is the force it experiences

In the 2nd equation, q is the charge emitting the field}

What is the equation for the force experience by a charge when placed in an electric field?

F = q_oE

What is the equation for electric potential energy?

U = (kqQ) / r Where q and Q are the two charges and r is the distance between them

What is electric potential? What is the equation to find it?

Electric potential and electric potential energy are very different things. Electric potential is the ratio of the magnitude of a charge's electric potential energy to the magnitude of the charge itself V = U / q or V = k (Q/r)

What is the equation for the measurement of current? What is the SI unit of current?

i = (∆q / ∆t) Ampere

What is the equation for a magnetic field generated by current running through a straight wire?

B = (μ_o i ) / (2 π r ) μ_o is the constant 4π x 10^-7 r is the distance from the wire

What is the magnitude of a magnetic field generated by current moving through a loop of wire?

B = (μ_oi) / 2r Where r is the radius of the loop of wire

What is the equation for the force exerted on a moving charge as it passes through a magnetic field?

F = qvBsinƟ q is the charge, v is its velocity, and Ɵ is the smallest angle between the charge velocity and the magnetic field vector

What is the equation for the resistivity of a conductive material?

R = (*p* L ) / A Where *p* is the resistivity constant, L is the length, and A is the cross sectional area

If given the voltage drop and current across a resistor, what's the equation to find energy dissapated?

P = iV

If given the current and resistance across a resistor, what's the equation to find the power disappated?

P = i²R

What's the equation for determining a capacitor's capacitance from charge and voltage?

C = Q/V

What's the equation for the electric field inside a capacitor?

E = V/d Where d is the distance between the plates

What is the equation for the potential energy stored inside a capacitor?

U = (1/2)CV²

What is Hooke's Law?

Hooke's law is the equation for the restoring force of a distended spring: F = -kx Where x is the displaced distance and k is the spring constant

How do you calculate the acceleration of a displaced spring?

Angular momentum: a = - ω²x ω = 2πf = sqrt(k/m)

A spring is compressed but not released. What is the equation for spring potential energy?

U = (1/2)kx²

When a pendulum is swung away from its resting position, what equation shows its restoring force?

F = -mgsinθ

What's the equation for a standing wave and the length of an open pipe that supports it?

λ = 2L / n Where L is the length of the pipe and N is a nonzero integer

What is the equation for a closed pipe and the wavelength contained?

λ = ( 4L / n )

In a mirror, what is the equation to calculate image distance?

(1/d_object) + (1/d_image) = (1/d_f)

What's the equation for finding the magnification of an object?

m = - (image size / object size)

What's the equation for finding the critical angle for total internal reflection?

sinθ_c = (n₂ / n₁)

What's the equation for locating the maxima of a slit interference pattern?

dsinθ = mλ where m is a whole number refering to the maxima

What's the equation for locating the minima of a slit defraction pattern?

dsinθ = ( m + 1/2 ) λ

What's the equation for calculating the energy of a photon?

E = *hf* Where h is Plank's constant and *f* is the frequency

What's the equation to find the equilibrium constant?

K_eq = [C]^c[D]^d / [A]^a[B]^b

What's the equation to find ∆G?

∆G = ∆H - T∆S T is in Kelvin ∆G is Gibbs free energy

Given ∆H and ∆S values, how can you tell if a reaction is spontaneous or non spontaneous?

If ∆H and ∆S are (-) then spontaneous only at low temps If ∆H and ∆S are (+) then spontaneous only at high temps If ∆H is + and ∆S is - then nonspontaneous If ∆H is - and ∆S is + then always spontaneous

What's the equation to find stardard free energy change for a reaction?

∆G_rxn = -RT ln K_eq

What are standard temperature and pressure?

273.13 K (0^o C) and 1 atm

One mole of a gas will take up _____ liters at STP

22.4

What is Boyle's Law?

At constant temperature, a gas's volume is proportional to its pressure. p₁v₁ = p₂v₂

How do you find the partial pressure of a gas in a given gaseous mixture?

Partial pressure is the pressure of the gas multiplied by the mole ratio.

What are colligative properties? How many are there?

Colligative properties are the physical aspects of solutions that are dependent on the concentration of dissolved particles. They are: * vapor pressure depression * boiling point elevation * freezing point depression * osmotic pressure

What's the equation to calculate change in vapor pressure due to solute added?

∆P = X_AP^o_A X_Ais the mole ratio of solvent and P^o is the vapor pressure of the pure solvent

What's the equation for boiling point elevation / freezing point depression due to the adding of a solute?

∆T = iK_bm m is ***molality***, K_b is the constant for the solvent, and i is the Van't Hoff factor

What is the equation for solubility product constant?

For A_xB_y --\> xA + yB Ksp = [A]^x[B]^y

Equations (by definition) Flashcards

(70 cards)