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29 Cards in this Set
- Front
- Back
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E
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Energy
physical quantity that provides a measure of the state of a system |
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E (unit of measure)
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J, joule
J = Nm J = kg * m/2² * m |
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K definition
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Kinetic Energy
describes motion of a system |
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K formula (straight line)
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K = 1/2 * m * v²
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K formula (rotational)
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K = 1/2 ω²
where ω² is measured in rad / s |
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Relationship of velocity to K
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K increases as the square of v
as v doubles, K quadruples |
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F_g
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force exerted by gravity
F_g = G * (m₁ * m₂ ₂/ r²) Force of gravity = gravitational acceleration * product of masses / square of radius |
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U_g
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gravitational potential energy
9.8 m / s² OR 9.8 N / kg form of energy describing interaction between an object and the earth (or a reference level) PE stored due to relation of object to reference level |
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U_g formula
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U_g = m g y
gravitational PE = mass * gravitational acceleration * height above reference level |
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U_e
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elastic potential energy
energy stored in a system as a result of its deformation ideal model is a spring |
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U_e formula
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U_e = 1/2 k x²
where k = spring constant |
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Hooke's Law
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F = k x
Force exerted by a spring = spring constant * length between equilibrium point and stretch/compress point |
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E_th
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thermal energy, released as heat
energy associated with molecular motion |
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Heat
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arises due to difference between the vibratory motion of a system's molecules relative to the molecules in the environment
occurs when T_sys != T_env |
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E_chem
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chemical energy stored in fuel
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∑E for class
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∑E = K + U_g + U_e + E_th + E_chem
a system may have all or only some of these |
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How can E be changed?
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system must interact with environment
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W
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work
physical quantity describing how a system interacts with its environment to produce a ∆ in ∑E_sys written script style to differentiate between W for weight |
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W (algebraic formula)
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W = F d cos θ
work = force applied * displacement * cos of angle between force & displacement |
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Work-Energy Theorem
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W = ∆E
W = ∆K + ∆U_g + ∆U_e + ∆E_th + ∆E_chem |
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Work between system & its environment
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Work done BY system
increases E of environment, decreases E of system work done ON system increases E of system, decreases E of environment |
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Law of Conservation of Total Energy
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In absence of work done on/by system, ∑E remains constant
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Work's relation to motion
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inhibit motion < W = 0 < enhance motion
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K = 1/2 m v² manipulations
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v = √(2K / m)
m = 2K / v² |
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F_n or n
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normal force
The component of a contact force exerted on an object that is perpendicular to the surface the pressure a table exerts on a book the pressure a ramp exerts on a wheelchair |
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W
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weight (can also mean work, written script style in class to denote work)
W = mg Weight = mass * gravitational acceleration |
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ME
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mechanical energy
ME = K + U_g + U_e |
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Student standing on roof throws ball of m=0.5 kg vertically upward at 20 m/s at h=100 m above the ground. Neglect air resistance. Find
a. speed of impact of ball on ground (point B) b. maximum elevation (point C) c. total flight time |
Define system to include everything
a W=0=∆E ∆E = ∆K+∆U_g =[(1/2 m v_B²) - (1/2 m v_A²)] + [(m g y_B) - (m g y_A)] disregard m since it is in every term, reduce & simplify 0=(1/2 v_B²) - (1/2 (20 m/s)²) + 9.8*0 - 9.8*100 b same equation, use points A & C, solve for y_C c needs kinematics v_yf = v_yi + a_y * ∆t solve for ∆t ∆t = (v_yf - v_yi) / a_y |
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If W = 0 J, and only ME exists, then
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0 J = ∆K + ∆U_g + ∆U_e
since energy is never created or destroyed, only converted, ∑E_final = ∑E_initial K_final + U_g_final + U_e_final = K_initial + U_g_initial + U_e_initial |
