Physics Second Semester Exam Review 2014 Honors and Physics Classes Momentum Inertia in motion. p = mv Must be moving. No velocity, no momentum. Mass and velocity are both directly proportional to momentum. Change in momentum Formula: Δ p = mv f mv i Impulse equals a change in momentum. J = F t F t = Δ p F t = mv f mv i The time force applied is important. The longer the time, the less force in the change of momentum. Momentum is conserved. Collisions Elastic collisions-objects bounce off each other. 1. no heat released 2. no sound produced 3. no deformation (these 3 conditions only occur at the atomic level) (known as perfectly elastic) 4. Formula Before = After v v v v m 1 + m 2 = m 1 + m 2 1
Inelastic collisions-objects stick together 1. heat produced 2. sound produced 3. deformation occurs 4. Formula Before = After v v )v m 1 + m 2 = (m 1 + m 2 Kinetic Energy is conserved in Elastic Collisions 1mv 2 1 1 + mv 2 1 2 2 + mv 2 1 2 1 + 2 mv22 2 Sample Questions What is the momentum possessed by a car with a mass of 2 350 kg if it is traveling at 125 km/h? What impulse is required to stop a 0.25 kg baseball traveling at 52 m/s? (b) If the ball is in the fielder s mitt for 0.10 seconds as it is being stopped, what average force was exerted on the ball? We see a 15 000 kg railroad car moving along the track at 2.5 m/s. It collides and couples with a stationary 12 500 kg car. What is the new velocity of the two cars? 2 mud balls collide in a perfectly elastic collision. One has a mass of 4.0 kg, the second has a mass of 3.5 kg. The first one has an initial velocity of 3.4 m/s, the second has an initial velocity of 4.8 m/s. What is their velocity after the collision? Heat and Thermodynamics Temperature The average amount of kinetic energy in a substance. Adding or removing energy usually changes temperature. Temperature scales 1. Fahrenheit T F = ( 5 9 T ) 2 C + 3 2. Celsius T C = 9 5 (T 2) F 3 2
Internal Energy Heat Specific Heat Capacity 3. Kelvin (SI) K = T C + 273 Kelvin is not measured in degrees. It is a value. the energy of a substance due to the random motions of its component particles and equal to the total energy of those particles. Heat is the flow of energy based on temperature difference. Heat does not flow if there is no change in temperature. This is known as thermal equilibrium. Units of heat. joule - SI unit calorie Calorie Conversions 1 calorie is 4.186 J/g o C 1 Calorie is 4186 J/kg o C Specific heat is the amount of energy needed to raise the temperature of 1 g of a substance by 1 o C Formula Q = m cδt Q-quantity of heat m-mass c-specific heat Δ T -change in temperature Δ T = T f T i Specific heat of various substances water - 4.186 J/g o C, 1c/g o C steam - 2.01 J/g o C ice - 2.09 J/g o C copper - 3.87 J/g o C Quantity of heat Q Lost = Q Gained Sample Questions 34 000 J of heat is added to a 2.5 kg sample of water. What is the temperature change that takes place? 3
A 235 g gold ball at a temperature of 125 C is dropped into an insulated flask of water. The water was initially at a temperature of 22 C. If the equilibrium temperature is 25 C, what is the mass of the water? A 158.0 g brass ball at a temperature of 265 C is dropped into a container containing 550.0 g of water. If the final temperature of the ball is 35.5 C, what was the initial temperature of the water? How much heat is required to melt 2.85 kg of ice at zero degrees Celsius? Latent Heat The amount of heat necessary for a phase change. Heat of fusion-heat for melting/freezing H f =3.35x10 5 J Q = mh f Heat of vaporization-heat for boiling/condensing H v =2.26x10 6 J Q=mH v Thermodynamics Putting heat energy to work. Zeroth Law of Thermodynamics Three object in contact, if two of the objects are in equilibrium, then the third object is equilibrium as well. First Law of Thermodynamics Energy cannot be created nor destroyed. Formula Δ U = Q W Second Law of Thermodynamics Law of entropy. Entropy is when disorder increases. Heat escapes from a system. Heat engines 4
A steam engine operates on a warm 28.0 C day. The saturated steam operates at a temperature of 100.0 C. What is the ideal efficiency for this engine? Waves Vibrations back and forth motion that causes a wave to form. energy Waveforms Crest-top part of the wave Trough-bottom part of the wave wavelength-two consecutive points on a wave amplitude-distance from equilibrium to crest or trough. Shows energy of the wave. Types of waves Transverse wave-energy and medium are at right angles to each other. Longitudinal wave-energy and medium are along the same line. Formula v = λ f 5
Simple Harmonic Motion Simple back and forth motion. small degrees (13 o on a pendulum) Pendulum motion formula: T = 2 π g l Spring Motion formula: T = 2 π m k Interference Constructive interference: two waves superimpose. Crest on crest, trough on trough Destructive interference: two waves superimpose, crest on trough Resonance 6
Resounding: one object causes another to vibrate. Based on frequency. Standing waves Light and Reflection Light comes to us from the Sun in the form of Electromagnetic Waves. Light travels at a speed of 3x10 8 m/s, or 300,000 km/s, or 186,000 mi/s. This speed is constant for the universe. Formula: c = λ f Electromagnetic Spectrum Frequency and Energy increase from Radio to Gamma waves. Wavelength decreases from Radio to Gamma waves. Experiments to test the speed of light. Roemer s experiment using Jupiter and Io. Michelson s experiment using revolving mirror. 7
Reflection Law of Reflection The angle of incidence is equal to the angle of reflection. Diffuse Reflection: scattered reflection due to a rough surface. Specular Reflection: smooth reflection due to a smooth surface. Flat Mirrors Flat mirrors direct light specularly. Images are the same distance from the mirror as the object. Images are always virtual and the same size as the object. A virtual image is upright. Use the Law of Reflection to draw diagrams. Curved Mirrors A curved mirror is a portion of a reflecting sphere. The focal point is F. The center of curvature C is equal to the radius R. Sample Question 8
A concave mirror has a focal length of 10.0 cm. What is its radius of curvature? (20 cm) Two types of curved mirrors. Concave Convex Images may be real or virtual depending on placement of object. Rules for Ray Diagrams 1. A ray parallel to the principal axis reflects through the focal point. 2. A ray travelling through the focal point reflects parallel. 3. A ray travelling through C reflects back along itself. Mirror Equation Sign Convention R: radius of curvature...+ for converging, - for diverging f: focal length...+ for converging, - for diverging di: image distance...+ for real images, - for virtual images hi: image height...+ if upright, - if inverted Refraction The bending of light as it passes from one medium to another. The refraction is due to the change in velocity of a different medium Index of Refraction: The ratio of velocity of light in a vacuum compared to the light in a medium. 9
Formula: n = v c c = 3.x 10 8 m/s Sample Questions The speed of light in a plastic is 2 x10 8 m/s. What is the index of refraction of the plastic? Find the velocity of yellow light in a diamond whose refractive index is 2.42. Indices of Refraction for Light Medium n Medium n vacuum 1.00 crown glass 1.52 air 1.00 quartz 1.54 water 1.33 flint glass 1.61 ethanol 1.36 diamond 2.42 Snell s Law n 1 sinθ 1 = n 2 sinθ 2 When moving from a less dense medium to a more dense medium, light bends towards the normal. When moving from a more dense medium to a less dense medium, light bends away from the normal. Thin Lenses Converging lenses: thicker in the middle 10
Diverging lenses: thinner in the middle Image formation Images formed from a converging lens can be real or virtual. If the object is outside the focal point, image is real. If the object is inside the focal point, image is virtual. Lens Equation Same as for mirrors. Sign Convention R radius of curvature + for converging, - for diverging f focal length + for converging, - for diverging d i image distance + for real images, - for virtual images h i image size + if upright, - if inverted Electrostatic Electromagnetic force is a fundamental force in the universe. As electrons move, objects gain a charge. An excess of electrons will give a negative charge. A deficit of electrons will give a positive charge. Like charges repel: Opposite charges attract. Conservation of charge: charge is not created or destroyed, just transfered from one system to another. Charging Objects Charging by Conduction friction. Electrons transfer from one object to another. 11
Charging by Induction Objects are charged even though they do not touch. Charges line up Polarization Coulomb s Law Symbol for charge is q. (Q for a large amount of charge) Unit of charge is the Coulomb. C An elementary particle is a proton or electron. One Coulomb is equal to 6.25x10 18 elementary particles. The charge of an elementary particle 1.6x10-19 C Charged objects exert forces on one another. The force is directly proportional to the magnitude of the charges. The force is inversely proportional to the magnitude of the distance squared between the two charges. Formula kq F = 1 q 2 r 2 Coulomb s Constant k = 8.99x10 9 Nm2 / C2 Sample Problem Two point charges are 5.0 m apart. If the charges are 0.020 C and 0.030C, what is the force between them and is it attractive or repulsive? Let s look at a system of three charges. The charges are arranged as shown in the drawing. q 1 is 3.00 m from q 2. q 2 is 4.00 m from the q 3. (We immediately spot this as one of those 345 triangle deals, so we know that q 1 is 5.00 m from q 3 ). What is the net force acting on q 3? 12
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