Chapter 11: Fluids. ρ = Density: Pressure: F P = P atm = Pa = 1 atm. Pressure: Pressure in a Static Fluid: P2 = P1+

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1 Chapter 11: Fluids Density: ρ = m V ρ = 1. 1 water 3 kg m 3 Pressure: Pressure: F P = P atm = Pa = 1 atm A Pressure in a Static Fluid: P = P1+ ρ gh Pascal s Principle: Any change in the pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and the enclosing walls Buoyancy: Archimede s Principle: the magnitude of the buoyant force on an object partially or completely immersed in a fluid equals the weight of the fluid displaced Buoyant Force: FB = ρ fluidvsubg if an object is completely submerged, V sub = V obj if an object is floating, F B = w = mg Fluids in Motion: Equation of Continuity: ρ1av 1 1 = ρav if the fluid is incompressible (ρ 1 =ρ ): Av 1 1= Av Bernoulli s Equation: P1+ 1 ρv ρgy1 = P + ρv + ρgy Bernoulli s Principle: where the speed of a fluid increases, the pressure in the fluid decreases

2 Chapter 16: Waves and Sound Waves: Transverse Wave: the disturbance occurs perpendicular to the direction of travel of the wave Longitudinal Wave: the disturbance occurs parallel to the direction of travel of the wave f 1 1 = T = T f λ v = v = λ f T if the frequency is increased, the wavelength is decreased but wave speed doesn t change Speed of waves on a string: v = F ( m/ L) Doppler Effect: f = v 1± f v s v 1 s v Numerator: + observer moving toward source - observer moving away from source Denominator: - source moving toward observer + source moving away from observer

3 Chapter 17: Linear Superposition and Interference Linear Superposition: The Principle of Linear Superposition: when two or more waves are present at the same place at the same time, the resultant disturbance is the sum of the disturbances from the individual waves for wave sources vibrating in phase: Beats: Δ L= nλ n =,1,,... constructive interference Δ L= ( n+ 1 ) λ n =,1,,... destructive interference f = f f beats 1 Standing Waves: for standing waves on a string fixed at both ends: L v λ = fn = n n = 1,,3,... n L

4 Chapter 5: The Reflection of Light The Reflection of Light: in optics, all angles are measure with respect to the normal Law of Reflection: θ r = θ i Images from Plane Mirrors: the image created by a plane mirror is virtual, upright, the same size as the object, and as far behind the mirror as the object is in front of it Images from Spherical Mirrors: a convex mirror always produces a virtual, reduced, and upright image a concave mirror can produce a: real, enlarged, inverted image (if object is between C and F) real, reduced, inverted image (if object is beyond C) virtual, enlarged, upright image (if object is between F and mirror) from a single mirror, real images are always inverted and virtual images are always upright. Mirror and Magnification Equations: mirror equation: hi di + = magnification equation: m = = d d f h d o i o o f > concave mirror f < convex mirror d o > real object (in front of mirror) d o < virtual object (behind mirror) d i > real image (in front of mirror) d i < virtual image (behind mirror) m > image is upright m > 1 image is enlarged m < image is inverted m < 1 image is reduce

5 Chapter 18: Electric Forces and Fields m p = kg m n = kg m e = kg charge on a proton: q p = +e = C charge on an electron: q e = -e = C charge is quantized: q = + ne n =, 1,, Charged Objects: Law of Conservation of Electric Charge: during any process, the net electrical charge of an isolated system remains constant like charges repel and unlike charges attract each other there are three ways to charge an object: charging by friction, charging by induction, and charging by contact Coulomb s Law: F kq q k r 1 = = 9 Nm C the direction of the force is along a line connecting the two charges if there are more than two charges, the net force on a charge is the vector sum of all the forces on the charge The Electric Field: the electric field is defined as: F E = q where q is a small test charge the force on a charge in an electric field is given by: F = qe kq the electric field from a point charge is given by: E = r E points away from a positive charge E points toward a negative charge

6 Chapter 31: Nuclear Physics and Radioactivity Nuclear Structure: a special notation is used to indicate the composition of a nucleus: A Z X Atomic number Z: # of protons in nucleus Atomic mass number A: # of protons + # of neutrons (N) X: chemical symbol for element A = Z + N the average radius of a nucleus of atomic mass number A is give by: r (1. 1 m) A Radioactivity: there are three types of particles given off during the various processes of radioactive decay: α particle He ( protons and neutrons) β particle 4 β β γ-ray γ - -1 e + +1 e (electron) (positron) (high-energy photon) α decay: P D+ He A A-4 4 Z Z- β decay: P D+ e+ υ A A Z Z+1 1 e + β decay: P D+ e+ υ A A Z Z e γ decay: P P+ γ A * A Z Z Radioactive decay: λt Nt ( ) = Ne N # of unstable nuclei λt At ( ) = Ae A activity.693 λ = T 1 Nuclear Binding Energy: Binding energy: E B = (total energy of Z protons + N neutrons) (total energy of nucleus) E B = (Δm)c Mass Defect: Δm = (mass of Z protons + N neutrons) (mass of nucleus) if masses are in atomic mass units (u), you can use the following conversion: c = MeV/u