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Final Review Lecture

Final Review Lecture. Remember: Final is at 9 am Monday, December 7 . Chapter 1 Units and density The three basic units are meters, kilograms and seconds Density is mass/volume: ρ=m/V Chapter 2 One-dimensional motion

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Final Review Lecture

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  1. Final Review Lecture Remember: Final is at 9 am Monday, December 7

  2. Chapter 1 Units and density The three basic units are meters, kilograms and seconds Density is mass/volume: ρ=m/V Chapter 2 One-dimensional motion The three basic measures of motion are displacement, velocity and acceleration For constant acceleration, position (s) vs. time is a parabola: s-s0=v0t-½at2 Chapter 3 Vector math The three basic vector operations are addition, dot products and cross products addition→vector in plane, dot→scalar, cross→vector perpendicular to plane Chapter 4 Three-dimensional motion Projectile trajectory depends on angle and velocity: y=(tanθ)x-gx2/2(v0cosθ)2 Uniform circular motion causes centripetal acceleration: a=v2/r Chapter 5a Frictionless free-body diagrams Along each axis, net force is mass×acceleration: ∑Fx=max, ∑Fy=may Action-reaction force pairs act on different bodies (Newton’s Third Law)

  3. Chapter 5b and 6 Free-body diagrams with friction Normal force→perpendicular to surface; friction→parallel (surface area no effect) Friction force is normal force×coefficient of friction (static or kinetic): fs,k=ms,kn Chapter 7a Kinetic energy (K) Kinetic energy quantifies an object’s translational state: K=½mv2; Power: P=Fv Positive work done by an object (hand) transfers energy to system (brick+earth) Chapter 7b Potential energy (U) Potential energy quantifies an object’s configurational state: U=mgh or U=½kx2 Total energy is conserved: W=ΔE=(K+U+Ethermal+Einternal)f-(K+U+Eth+Eint)i

  4. Chapter 9 Linear momentum and collisions Along each axis the center of mass is mass(fraction)×distance, e.g. xcom=1/M∑mixi Linear momentum is mass×velocity: p=mv, and is conserved Collisions conserve momentum, elastic collisions also conserve energy Impulse, J, is the momentum change, or the area under a force vs. time curve Chapter 10 Simple rotations and torque Transfer all concepts from linear frame to rotational frame, e.g. force→torque s=θr, v=ωr, a=αr=ω2r; I=∑mir2i , K=½Iω2, τ=r×F =Iα, W=∫τdθ, P=τω, I=Icom+Mh2 Chapter 11 Rolling rotations and angular momentum Rolling is “perfect” combination of rotation and translation Angular momentum, l=r×p orL=Iω, is conserved; τ=dL/dt (Newton’s 2nd law) Chapter 12 Free-body diagrams with torque In equilibrium, net force and net torque equal zero The three elastic moduli (Young’s, shear, and bulk) equal stress÷strain

  5. Chapter 13 Gravity Gravitational force follows the inverse square law: F=GMm/r2 and U=-GMm/r Kepler’s Laws: planet move in ellipses, sweep equal areas/time, T2=(4p2/GM)r3 Chapter 14 Fluid statics and dynamics Pressure, P, is force÷area (increases with depth by ρgh), Fbuoyant=m(fluid displaced)g Dynamic flow follows continuity and Bernoulli equations: Av, p+½ρv2+ρgh=cnst. Chapter 15 Time-dependant oscillations Period, T, is (frequency)-1 or 2p/ω; f(t)=Acos(ωt+φ), solves differential equation Pendulums: T=2p(L/g) -½ or 2p(I/mgh) -½ for simple and physical, respectively Chapter 16 Time and distance dependant waves Transverse and longitudinal sine waves (can be both: water), f(x,t)=Asin(kx-ωt+φ) Chapter 17 Sound waves in elastic medium Resonance occurs at frequencies=nv/2L (n integer) for (anti)nodes at both ends Doppler effect reduces/increases frequencies for departing/approaching sources Chapter 18 Superposition and standing waves Standing wave: 2Asin(kx)cosωt; any wave’s velocity is (elasticity÷inertia) -½

  6. The uniform rod shown below is held in place by the rope and wall. Suppose you know the weight of the rod and all dimensions. Then you can solve a single equation for the force exerted by the rope, provided you write expressions for the torques about the point: A) 1 B) 2 C) 3 D) 4 E) 1, 2, or 3

  7. 3) The ideal mechanical advantage (i.e. the ratio of the weight W to the pull P for equilibrium) of the combination of pulleys shown is: A) 1 B) 2 C) 3 D) 4 E) 5

  8. 2) The pull P is just sufficient to keep the 14-N block and the weightless pulleys in equilibrium as shown. The tension T in the upper cable is: A) 14 N B) 28 N C) 16 N D) 9.33 N E) 18.7 N

  9. 4) To shear a cube-shaped object, forces of equal magnitude and opposite directions might be applied: A) to opposite faces, perpendicular to the faces B) to opposite faces, parallel to the faces C) to adjacent faces, perpendicular to the faces D) to adjacent faces, neither parallel or perpendicular to the faces E) to a single face, in any direction

  10. 5) A projectile is fired straight upward from Earth's surface with a speed that is half the escape speed. If R is the radius of Earth, the highest altitude reached, measured from the surface, is: A) R/4 B) R/3 C) R/2 D) R E) 2R

  11. 6) A planet is in circular orbit around the Sun. Its distance from the Sun is four times the average distance of Earth from the Sun. The period of this planet, in Earth years, is: A) 4 B) 8 C) 16 D) 64 E) 2.52

  12. 7) The period of a simple pendulum is 1 s on Earth. When brought to a planet where g is one-tenth that on Earth, its period becomes: A) 1 s B) C) 1/10 s D) E) 10 s

  13. 8) Five hoops are each pivoted at a point on the rim and allowed to swing as physical pendulums. The masses and radii are hoop 1: M = 150g and R = 50 cm hoop 2: M = 200g and R = 40 cm hoop 3: M = 250g and R = 30 cm hoop 4: M = 300g and R = 20 cm hoop 5: M = 350g and R = 10 cm Order the hoops according to the periods of their motions, smallest to largest. A) 1, 2, 3, 4, 5 B) 5, 4, 3, 2, 1 C) 1, 2, 3, 5, 4 D) 1, 2, 5, 4, 3 E) 5, 4, 1, 2, 3

  14. 9) A certain spring elongates 9 mm when it is suspended vertically and a block of mass M is hung on it. The natural frequency of this mass-spring system is: A) 0.014 B) 5.3 Hz C) 31.8 Hz D) 181.7 Hz E) need to know M

  15. 10) The mathematical forms for the three sinusoidal traveling waves are gives by wave 1: y(x,t) = (2 cm) sin (3x – 6t) wave 2: y(x,t) = (3 cm) sin (4x – 12t) wave 3: y(x,t) = (4 cm) sin (5x – 11t) where x is in meters and t is in seconds. Of these waves: A) wave 1 has the greatest wave speed and the greatest maximum transverse string speed B) wave 2 has the greatest wave speed and wave 1 has the greatest maxmium transverse string speed C) wave 3 has the greatest wave speed and the greatest maximum transverse string speed D) wave 2 has the greatest wave speed and wave 3 has the greatest maximum transverse string speed E) wave 3 has the greatest wave speed and wave 2 has the greatest maximum transverse string speed

  16. 11) A 40-cm long string, with one end clamped and the other free to move transversely, is vibrating in its fundamental standing wave mode. The wavelength of the constituent traveling waves is: A) 10 cm B) 20 cm C) 40 cm D) 80 cm E) 160 cm

  17. A sinusoidal wave is traveling toward the right as shown. Which letter correctly labels the wavelength of the wave? A) A B) B C) C D) D E) E

  18. A standing wave pattern is established in a string as shown. The wavelength of one of the component traveling waves is: A) 0.25 m B) 0.5 m C) 1 m D) 2 m E) 4 m

  19. 14) Two notes are an "octave" apart. The ratio of their frequencies is: A) 8 B) 10 C) D) 2 E)

  20. 15) A stationary source emits a sound wave of frequency f. If it were possible for a man to travel toward the source at the speed of sound, he would observe the emitted sound to have a frequency of: A) zero B) f/2 C) 2f/3 D) 2f E) infinity

  21. 16) The "A" on a trumpet and a clarinet have the same pitch, but the two are clearly distinguishable. Which property is most important in enabling one to distinguish between these two instruments? A) intensity B) fundamental frequency C) displacement amplitude D) pressure amplitude E) harmonic content

  22. 17) The pressure exerted on the ground by a man is greatest when: A) he stands with both feet flat on the ground B) he stands flat on one foot C) he stands on the toes of one foot D) he lies down on the ground E) all of the above yield the same pressure

  23. Take the speed of sound to be 340 m/s. A thunder clap is heard about 3 s after the lightning is seen. The source of both light and sound is: A) moving overhead faster than the speed of sound B) emitting a much higher frequency than is heard C) emitting a much lower frequency than is heard D) about 1000 m away E) much more than 1000 m away

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