Review for Midterm 3

1. Review for Midterm 3 • Announcements: • I'm having a problem on #8 part A for tomorrow night's homework. It doesn’t seem like my numbers work out geometrically. My "d" value is 2 meters, and my total string length is 3.7 meters, meaning that each side of the triangle has to be 0.85m. So when I tried to form a right triangle to figure out the tensions, I get a hypotenuse (0.85m) that is smaller than one of my sides (d/2 = 1m. Am I crazy or do these numbers not make sense? Thanks! • This might seem weird, but I think problem #8 on the current web assign is wrong, at least with the numbers they give me.  It has a triangle with sides 2, 0.8 and 0.8, which isn't possible.  I tried the same problem in the book and got the right answer there, but I do not know how to solve it on the web assign if the numbers do not add up. • I think something is wrong with the last webassign or im understading it wrong. Just the trig on it. The distance between the 2 pulleys is 2 meters for mine and the string lenght is less then 4 meters. There would not be enought string for it to reach the weight.

2. Conditions for static equilibrium (For extended objects) • The net force acting on the particle must be zero. • The net torque about any axis acting on the particle must be zero. • The angular and linear speeds must be zero.

3. Shear modulus: Young’s modulus: Bulk modulus:

4. G… constant G = 6.673·10-11 N·m2/kg2 m1, m2…masses of particles 1 and 2 r… distance separating these particles … unit vector in r direction Universal Gravitation Gravitational potential energy • Notice the – sign • U = 0 at infinity • U will get smaller (more negative) as r gets smaller. • “Falling down” means loosing gravit. potential energy. • Use only when far away from earth; otherwise use approximation U = mgh.

5. Kepler’s laws: • Planets move in elliptical paths around the sun. The sun is in one of the focal points (foci) of the ellipse • The radius vector drawn from the sun to a planet sweeps out equal areas in equal time intervals (Law of equal areas). III. The square of the orbital period, T, of any planet is proportional to the cube of the semimajor axis of the elliptical orbit, a. Area S-A-B equals area S-D-C

6. Buoyant forces and Archimedes's Principle Case 1: Totally submerged objects. If density of object is less than density of fluid: Object rises (accelerates up) If density of object is greater than density of fluid: Object sinks. (accelerates down). Archimedes’ principle can also be applied to balloons floating in air (air can be considered a liquid)

7. Bernoulli’s equation Conservation of energy

8. Properties of simple harmonic motion Displacement: Angular frequency: Frequency: Period T: Units: 1/s = 1 Hz Velocity: Acceleration:

9. Energy of harmonic oscillator Kinetic energy: Potential energy: Total energy:

10. The physical pendulum The pendulum

11. Traveling waves • Crest: “Highest point” of a wave • Wavelength l: Distance from one crest to the next crest. • Wavelength l: Distance between two identical points on a wave. • Period T: Time between the arrival of two adjacent waves. • Frequency f: 1/T, number of crest that pass a given point per unit time

12. Reading quiz question Can we just actually do a problem in class really quickly and find Phi? I still dont exactly get it but if you just go through it really quickly with actual numbers instead of just explaining the general idea again maybe I could get it. Thanks Problem 1, from last night’s HW

13. In gas and liquids: In solids: On string: B=Bulk modulus of medium, T=Tension, Y=Young’s modulus, r=density of material TC … air temperature in degrees Celsius

14. Both ends open: One end closed: Standing waves (both ends closed) Phase-shifted waves (traveling same direction) + + = =

15. Reading quiz question In the following question, how do you find the the three smallest x values corresponding to the antinodes: Two sinusoidal waves combining in a medium are described by the following wave functions, where x is in centimeters and t is in seconds.y1 = (5.0 cm) sin (x + 0.20t)y2 = (5.0 cm) sin (x - 0.20t)I don't understand the question conceptually

16. Doppler: slower than sound Moving source Both detector and source Moving detector + detector→toward source - detector→away from source + source→away from detector - source→towards detector + detector→toward source - detector→away from source + source→away from detector - source→towards detector Mach: faster than sound The ratio vS/v is called the Mach number.