Tentative Physics 1 Standards

Transcription

1 Tentative Physics 1 Standards Mathematics MC1. Arithmetic: I can add, subtract, multiply, and divide real numbers, take their natural and common logarithms, and raise them to real powers and take real roots. This can be with a calculator. MC2. Algebra: I can add, subtract, and multiply polynomials and rational expressions. I can solve linear and quadratic equations for one variable. This requires manipulating symbolic expressions; substituting numbers and letting a calculator solve it does not suffice. Students should know the quadratic formula or be able to solve quadratic equations by completing the square. MC3. Units: I can convert between different units for the same quantity; multiply and divide units of different quantities; and multiply and divide units of the same quantity. MC4. Vector Operations: I can add, subtract, take dot products and cross products, and find the magnitudes of vectors. Specifically for vectors specified as components in the same Cartesian system. MP1. Trigonometry: I can define the sine, cosine, and tangent functions relating the sides and angles of a right triangle. MP2. Vector components: I can convert between polar and Cartesian coordinate descriptions of vectors, and can convert between rotated Cartesian coordinates. MP3. Calculus: I can differentiate polynomial, rational, and logarithmic functions, and integrate polynomial functions and negative powers of a single variable. MP4. Small-angle approximation: I can estimate the sine, tangent, or cosine of a small angle given in radians. Kinematics KC1. Story: I can describe 1-D motion by equations, graphs, and words. Given one type of description, I can generate any other to describe the same motion. Graphs refer specifically to position-time, velocity-time, and acceleration-time graphs. Equations need be only qualitative, though students must be able to generate exact equations describing constant-velocity and constant-acceleration motion. KC2. x-v: I can relate absolute and relative position, velocity, and time in a 1-D constantvelocity situation. This includes creating the position or velocity equation given the other and appropriate initial conditions or other sufficient information, finding the differences between 9/3/13

2 positions and velocities of different constant-velocity objects, and finding the time at which particular events occur. KC3. x-v-a: I can relate absolute and relative position, velocity, acceleration, and time in a 1-D constant-acceleration situation. This expands the scope of the previous standard to include constant-acceleration situations. KP1. Ballistic: I can predict, calculate, and describe, and relate the horizontal and vertical components of position, velocity, and acceleration to time for a ballistic trajectory. This includes all free-fall projectile problems, including decomposing initial velocity vectors into components, deriving and using the range equation, finding the time at which particular events occur, determining the time and place of the apex of a trajectory, and so on. KP2. Circular: I can relate period, angular velocity, speed, position, and acceleration for an object undergoing uniform circular motion. This does not include circular motion with changing speed. Force (Key topic) FC1. N1: I can determine the unknown force in a system in mechanical equilibrium. Equate mechanical equilibrium and zero net force (Newton s first law). Also includes statics problems not involving torques. FC2. fbd: I can draw a qualitatively correct (appropriate forces with approximate directions and magnitudes) free-body diagram for a body in mechanical equilibrium and for a body with unbalanced forces. FC3. Net force: Given the individual vector forces acting on an object, I can determine the net force acting on it. FC4. N2: Given the net force acting on an object, I can determine its acceleration. FC5. Forces: I can determine the magnitudes and directions of the following forces: static and kinetic friction, normal force, tension, constant-field gravity, and a Hooke s law spring. This does not require finding the parallel and perpendicular components of an object s weight on an incline. FP1. Constraint: I can determine the components of forces in constrained systems and the magnitude and direction of forces of constraint. This includes finding the parallel and perpendicular components of an object s weight on an incline or a pendulum, and the magnitudes and directions of forces of constraint such as the normal force and tension. 2 9/3/13

3 Momentum (Key topic) PC1. N3: Given a force, I can identify its Newton s third law partner and the object it acts upon. PC2. J-p: I can relate the net force on an object, the force s duration, and the object s momentum change. This includes applying the impulse-momentum theorem, but does not require knowing the definition of impulse. PC3. p: I can relate the total momentum of a system of objects to the individual momenta of the objects in the system. PC4. p Conservation: I can apply conservation of momentum to analyze an isolated collision. This includes predicting final velocities, reconstructing initial velocities, and determining whether a collision is elastic, inelastic, or totally inelastic given sufficient information. It also includes relating initial and final total momentum. PP1. Conserved: Given the description of a collision, I can identify which physical quantities are conserved. (Momentum, kinetic energy, angular momentum.) Energy (Key topic) EC1. Work: I can relate the work done on an object to the applied force and the object s displacement. This includes being defining work. EC2. Net work: I can calculate the net work done by many forces acting on the same object. This can be either by adding the work done by each force or by finding the work done by the net force. Students should be able to use either approach and to know that they are equivalent. EC3. Kinetic: I can calculate the kinetic energy of an object from its speed and mass. EC4. Work-energy: I can relate the net work done on an object to its change in kinetic energy. This is the work-energy theorem. EP1. Energy conservation: I can use conservation of energy to analyze multi-step processes. Such processes include collisions, ballistic pendulums, Tarzan swinging on a vine, etc. EP2. Conservative Forces: I can identify and distinguish conservative and non-conservative forces. EP3. Energy Diagrams: I can interpret and apply energy diagrams. This includes knowing kinetic and potential energy at any position, qualitatively describing a trajectory given starting position and velocity, and describing the changes in any of these resulting from a change in total energy. 3 9/3/13

4 Rotors AC1. Torque: I can relate the torques and forces applied to a body, and I can relate the net torque to the individual torques. This includes the definition of torque, with full appreciation of its vector nature. It also includes applying the cross product. AC2. Angular N2: I can relate the net torque on a rotor to the rotor s moment of inertia and angular acceleration. This refers to angular Newton s first and second laws. It includes statics problems involving torques and cases of nonzero angular acceleration. AC3. Angular work: I can relate the rotational work done on a rotor to applied torque and angular displacement, and to the rotor s change in rotational kinetic energy. I can also relate the rotational kinetic energy of a rotor to its angular velocity and moment of inertia. These refer to the work-energy theorem in the angular case and to the formula K = 1/2 I 2. AC4. Angular momentum: I can relate a rotor s angular momentum to its moment of inertia and rotational velocity, and a particle s angular momentum to its momentum and its posiiton relative to a reference. These refer to the formulas L = I and L r = r p r. AP1. Angular kinematics: I can relate the angular velocity, angular position, and angular acceleration of a rotor undergoing a constant angular acceleration. AP2. Find I: I can calculate the moment of inertia of an object from its distribution of mass. This includes adding together segments of known angular momentum, looking up an angular momentum formula from a table and applying it properly, applying the parallel-axis theorem, and integrating to find the moment of inertia of a continuous body. AP3. L conservation: I can use conservation of angular momentum to analyze collisions involving rotors, and to predict the motion of an object whose moment of inertia changes. This includes collisions involving objects like swinging doors and pendulums, and to systems such as spinning ice skaters and bolas. Fluids VC1. Pressure: I can define pressure and density, explain how pressure varies with depth in a fluid, and calculate how pressure varies with depth in an incompressible liquid. Density = m/v; pressure p = F/A. Explain how pressure comes from the force of the fluid above; apply the formula p = p 0 + gh, VC2. Buoyancy: I can relate buoyancy, displaced volume, and density. Specifically, apply the relation F = gv. VC3. Flow: I can relate mass and volume flow rates, speed, and density, and can relate flow rates at different points in a fluid stream. Apply basic flow rate formulas dv/dt = va and dm/dt = 4 9/3/13

5 va. Apply the continuity equations, including rearranging a continuity equation to find an unknown. VP1. Bernoulli: I can use the Bernoulli equation to relate fluid pressure, height, and speed at different points. Also includes rearranging the Bernoulli equation to find an unknown, and eliminating zero terms to find special cases such as Torricelli s theorem. Gravity GC1. Big G: I can calculate the gravitational force between two particles. Apply Newton s gravitational formula. Specify direction as well as magnitude. GC2. Gravitational energy: I can calculate the gravitational potential energy between two particles and their total energy. GC3. Escape: I can calculate the escape speed of a particle in a gravitational well. Given the mass of the attractor and the distance from the center. GP1. Orbit: I can relate gravitational and centripetal forces for pairs of objects in circular orbits. This includes using these quantities to find unknowns such as orbital speed and period. GP2. Orbit conservation: I can use conservation of momentum, energy, and angular momentum to describe the motion of bodies in all types (circular, elliptical, parabolic, and hyperbolic) of orbit. Repeaters (Key topic) RC1. Phase angle: I can explain the meaning of the phase angle and the angular frequency used to describe a repeating process. RC2. SHM relations: I can identify the functional form of the net force on and the position of an object undergoing simple harmonic motion, and identify and explain the factors determining the frequency and amplitude of a simple harmonic oscillator. Includes knowing that Hooke s law describes the net force, that ma = kx is the governing differential equation, that a sinusoid x = A cos( t + ) is the general solution, and that frequency increases with k and decreases with m. RC3. SHM energy: I can describe the partitioning of energy at different phases of a simple harmonic oscillator or simple pendulum. Includes recognizing that mechanical energy is conserved, and that amplitude and maximum speed are monotonically related. RC4. Simple pendulum: I can identify and explain the factors determining the frequency and amplitude of a simple pendulum. Includes recognizing that frequency increases with g, 5 9/3/13

6 decreases as L increases, and does not depend on m. Does not include deriving the relation 2 = g/l or explicitly recognizing that the small-angle approximation is needed. RC5. Wave motion: I can define, identify, describe, and distinguish and transverse and longitudinal waves. Includes recognizing combinations of these limiting types, such as ocean waves. RC6. Interference: I can describe how standing waves and beats are generated, and can identify and describe nodes and antinodes of standing transverse and longitudinal waves. Includes defining and recognizing nodes and antinodes of different kinds of waves, including longitudinal waves. Applies only to waves propagating in one dimension, such as transverse waves in a rope and sound waves in a tube. RP1. SHM kinematics: I can relate the position, velocity, acceleration, frequency and period, amplitude, kinetic and potential energies, and phase of an object undergoing simple harmonic motion. Includes symbolically and quantitatively determining one equation of motion from another, and determining extreme values of any of the quantities. Includes integrating or differentiating the equations of motion and applying the formulas 2 = k/m and E = 1/2 ka 2 = 1/2 mv 2 max. RP2. Torsion: I can identify and explain the factors determining the frequency and amplitude of a torsional oscillator, including simple and physical pendulums. I can calculate the period of torsional oscillators, including physical pendulums. Includes applying the small-angle approximation. RP3. Damping: I can identify the characteristics of an oscillator that result in under-damping, critical damping, and over-damping, and explain the motion of a damped oscillator under those three regimes. Requires finding and interpreting the parameter ' 2 = k/m b 2 /4m 2, but does not require determining all the coefficients in the equations of motion. RP4. Propagation speed: I can relate the properties of a medium to the propagation speed of a wave in the medium. This includes the string transverse wave formula v = F µ and a qualitative understanding of the wave equation. RP5. Wave kinematics: I can relate the formulas for the displacement, velocity, and acceleration of a particle in a wave. I can explain how the equation y(x,t) = A cos(kx t+ ) describes position in transverse and longitudinal waves. I can relate the parameters of the equation to the wave s amplitude, frequency, period, wavelength, propagation speed, and initial phase. RP6. Intensity: I can explain and calculate the inverse-square relationship between sound intensity and distance from the source. I can relate sound intensity to the logarithmic decibel scale. RP7. Doppler: I can explain, calculate, and relate the received and emitted frequencies of a wave and the velocities of the source and detector. Apply the formula for non-relativistic Doppler shift. 6 9/3/13

7 Laboratories Lab 0 I can use the motion sensor and LoggerPro software to make x-t, v-t, and a-t plots of moving objects. I can use the LoggerPro software to calculate averages and slopes of recorded data. Lab 1 I can safely and responsibly operate the laboratory equipment. I can empirically determine a reliable estimate of the launch angle giving the largest range for trajectories ending at launch height and below launch height. I can empirically determine a reliable estimate of the launch angle giving the greatest projectile height at a given horizontal distance from the launch. Lab 2 I can make reasonably close accelerations form the same force and mass. I can experimentally test the relationship between net force, mass, and acceleration. Lab 3 I can experimentally test Hooke s law and communicate my findings in a clear, easy-to-follow format. I can experimentally correlate net force and acceleration using fan carts. I can relate the net force acting on a cart on an inclined track to the incline angle of its track. Lab 4 I can calculate my personal power from measurements of lifting a bowling ball. I can find the work done by a non-constant force by integrating force measurements along distance. I can experimentally relate net work and kinetic energy change. I can evaluate the constancy of mechanical energy of a body in a gravitational potential. Lab 5 I can evaluate conservation of momentum and kinetic energy in experimental collisions. Lab 6 I can experimentally compare a rolling objects acceleration down an incline to its theoretical acceleration. 7 9/3/13

8 Lab 7 I can experimentally compare the actual and theoretical acceleration of an Atwood machine with an inertial pullet. Lab 8 I can analyze the angular momentum and torques in a series of rotational collisions. Lab 9 I can investigate the effects of different experimental variables on the period of a pendulum. Lab A I can experimentally determine the density of a liquid form the buoyancy force it exerts on an immersed object. Lab B I can experimentally relate the nodal separation of a standing sound wave to its frequency, wavelength, and speed. I can identify the behavior of plane wave ripples, straight wave fronts, and single-slit and doubleslit interference. 8 9/3/13