Two capacitors are identical, except that one is empty and the other is filled with a dielectric (κ = 4.69). The empty capacitor is connected to a 11.0-V battery. What must be the potential difference across the plates of the capacitor filled with a dielectric so that it stores the same amount of electrical energy as the empty capacitor?

A particle of mass 5.00 kg is attached to a spring with a force constant of 210 N/m. It is oscillating on a frictionless, horizontal surface with an amplitude of 4.00 m. A 8.00-kg object is dropped vertically on top of the 5.00-kg object as it passes through its equilibrium point. The two objects stick together.
(a) What is the new amplitude of the vibrating system after the collision?_______________

(b) By what factor has the period of the system changed?______________
(c) By how much does the energy of the system change as a result of the collision?____________J

A red ball is thrown down with an initial speed of 1.3 m/s from a height of 27 meters above the ground. Then, 0.5 seconds after the red ball is thrown, a blue ball is thrown upward with an initial speed of 24 m/s, from a height of 0.8 meters above the ground. The force of gravity due to the earth results in the balls each having a constant downward acceleration of 9.81 m/s2

What is the speed of the red ball right before it hits the ground?

(Is it just jus the velocity equestion?)

How long after the red ball is thrown are the two balls in the air at the same height?

Maybe I am not doing something right, but this is what I have: 27 - 1.3t - 4.9t^2 = -4.9t^2 + 28.9t-12.425
with -4.9t^2 + 28.9t-12.425 being derived from .8 + 24(t-.5)-4.9(t-.5)^2 the only thing I can thing of would be to maybe to have it as 8 + 24(t+.5)-4.9(t+.5)^2 ?

Is the acceleration postive or negative and is speeding up or slowing down?

Using Stefan-Boltzmann and Wien laws

The Sun emits P = 4 10²⁶Watts, its radius is 6.95 10 ^8⁹m and its surface temperature T(Sun) = 5,800 K. We know that the Sun will gradually increase its power output in the future. We also know that its surface temperature will not change significantly, at least for a while. Using the law for the ‘black body’ radiation, find how much the Sun’s radius will change in %, if the power output of the Sun doubles.

An AC generator supplies an rms voltage of 115 V at 60.0 Hz. It is connected in series with a 0.550 H inductor, a 3.90 μF capacitor and a 311 Ω resistor. What is the impedance of the circuit?

What is the rms current through the resistor?

What is the average power dissipated in the circuit?

What is the peak current through the resistor?

What is the peak voltage across the inductor?

What is the peak voltage across the capacitor?

The generator frequency is now changed so that the circuit is in resonance. What is that new (resonance) frequency?

Make an experiment and answer the question below: 1. Place the can on its side on a flat smooth surface like a table or a smooth floor. 2. Rub the blown-up balloon back and forth through your hair really fast. 3. Now the fun part – Hold the balloon close to the can without actually touching the can. The can will start to roll towards the balloon without you even touching it! Try This Too: While you’ve got the balloon out, tear up part of tissue into tiny pieces about 1/4 inch (.5 cm) big. Rub the balloon on your hair again and bring it close to the tissue pieces. They will be attracted to the balloon and then jump away. When you rub the balloon through your hair, invisible electrons (with a negative charge) build up on the surface of the balloon. This is called static electricity, which means “non-moving electricity” The electrons have the power to pull very light objects (with a positive charge) toward them – like the soda can. to answer these questions: 1. Does the size of the balloon change the power of the pull? 2. Does the length of the person's hair affect the power of static electricity? 3. How much water can you put in the can until the balloon can’t pull it anymore?

Suppose the figure below represents a ray of light going from air through crown glass into water, such as going into a fish tank. Calculate the amount the ray is displaced by the glass (Δx in mm), given that the incident angle is 37.5° and the glass is 2.75 cm thick.

______ mm

A 3.50-kg ball, moving to the right at a velocity of +3.47 m/s on a frictionless table, collides head-on with a stationary 8.30-kg ball. Find the final velocities of (a) the 3.50-kg ball and of (b) the 8.30-kg ball if the collision is elastic. (c) Find the final velocity of the two balls if the collision is completely inelastic.

Suppose you are considering renting an apartment in a building in which the tenants are required to pay the cost of heating their apartments. The building has several apartments, each occupying an entire floor of the building. The building has a flat roof. You are attracted to the apartment on the top floor because of the view but your friend tells you that the heat bills will be higher for that apartment than for the ones on the lower floors.

a. [3pts] Is your friend likely to be right? Explain why or why not in terms of the expected thermal energy flows in and out of the apartments.

b. [4pts] Defend your answer to a. by calculating the amount of energy required to heat the top and lower apartments for a year in btu. Include the lowest apartment assuming that it is just above the ground (no basement below it). Suppose that the floor area of each apartment is 900 sq ft (30ft x 30ft) and that the height from one floor to the next is 10ft. Use 8500 as the number of ’degree days’ in Minnesota (Figure 5.12 and definition near the top of p. 137) and the R values given in Table 5-1 of the book (1978 values).

c. [3pts] Use the answer you got in b. to calculate the difference in cost (if any) between heating the top apartment for a year ,heating a lower apartment for year, and heating the ground floor apartment for a year, supposing that the cost of gas heating is $0.80 per ’therm’. 1 therm=100,000 btu.

10. A soap film (n = 1.33) is formed in a loop of wire that is mounted vertically is not exactly uniform in thickness because of its weight, but wedge-shaped in cross section. When the film is illuminated with green light of wavelength 520 nm, one sees that a distance of 2.40 cm separates two bright fringes that are 4 orders apart. By how much does the film differ in thickness over this distance?

In January 2006, astronomers reported the discovery of a planet comparable in size to the earth orbiting another star and having a mass of about 5.5 times the earth's mass. It is believed to consist of a mixture of rock and ice, similar to Neptune. Take mearth=5.97×1024kg and rearth=6.38×106m.

1) If this planet has the same density as Neptune (1.76 g/cm3), what is its radius expressed in kilometers?

Express your answer in kilometers.

2)

What is its radius expressed as a multiple of earth's radius?

Express your answer in units of earth's radius.

Horseshoe bats (genus Rhinolophus) emit sounds from their nostrils, then listen to the frequency of the sound reflected from their prey to determine the prey's speed. (The "horseshoe" that gives the bat its name is a depression around the nostrils that acts like a focusing mirror, so that the bat emits sound in a narrow beam like a flashlight.) A Rhinolophus flying at speed v bat emits sound of frequency f bat; the sound it hears reflected from an insect flying toward it has a higher frequency f refl.

If the bat emits a sound at a frequency of 80.9 kHz and hears it reflected at a frequency of 83.9 kHz while traveling at a speed of 3.8 m/s , calculate the speed of the insect.

Use 344 m/s for the speed of sound in air. Express your answer using two significant figures.

A hydraulic lift in a garage has two pistons: a small one of cross-sectional area 3.60cm2 and a large one of cross-sectional area 250cm2 .

a) If this lift is designed to raise a 3300-kg car, what minimum force must be applied to the small piston?

b)If the force is applied through compressed air, what must be the minimum air pressure applied to the small piston?

Let B = 5.40 m at 60.0°. C and A have equal magnitudes. The direction angle of C is larger than that of A by 25.0°. Let A · B = 27.9 m2 and B · C = 36.9 m2. Find the magnitude (in m) and direction (in degrees) of A.