A parallel-plate capacitor has capacitance C = 15.7 pF when the volume between the plates is filled with air. The plates are circular, with radius 2.50 cm. The capacitor is connected to a battery and a charge of magnitude 28.0 pC goes into each plate. With the capacitor still connected to the battery, a slab of dielectric is inserted between the plates, completely filling the space between the plates. After the dielectric has been inserted, the charge on each plate has magnitude 45.0 pC.

(a) What is the dielectric constant K of the dielectric?

(b) What is the potential difference between the plates before and after the dielectric has been inserted?

(c) What is the electric field at a point midway between the plates before and after the dielectric has been inserted?

Show that an atom with a filled subshell must have a ¹S₀ ground state.

A man is hiking at a park. At the beginning, he followed a straight trail. From the starting point, he traveled two miles down the first trail. Then he turned to his left by 30 degree angle to follow a second trail for one point five miles. Next, he turned to his right by 160 degree angle and follow a third trail for one point seven miles. At this point he was getting very tired and would like to get back as quickly as possible, but all of the available trails seem to lead him deeper into the woods. He would like to take a shortcut directly through the woods. How far to his right should you suggest him to turn, and how far do he have to walk, to go directly back to his starting point?

Q1: The man has to turn ____ degree to the right and walk ___ miles to the starting point.

Leaving home in the morning, I back down my driveway. Before entering the road, I realize I forgot my lunch and so I pull back in to my parking spot.

What is my velocity just before I realized I forgot my lunch and stopped?

What is my velocity the instant after I realized I forgot my lunch and started moving back

towards my parking spot?

A change in velocity is an acceleration. Did I accelerate, from the moment just before I

stopped the car to the moment just after I started moving back towards my parking spot?

Suppose you’re eating in yet another restaurant where the dishes are shared at the table and all placed uniformly on a rotating disk-like surface. Model this surface as a thin disk of radius 46.3 cm. Someone else has spun the surface, such that it is initially at an angular speed of 0.4 rev/s. The surface and food has a combined mass of 4.2 kg. The waiter, to show off, throws a new dish of dumplings (mass 0.9 kg) onto the surface at a speed of 0.7 m/s, such that the dish lands on and sticks to the very edge of the surface moving in the same direction as the rotating food. While this is happening, you quickly calculate the final angular speed of the food so that you can predict its location at any time before others have a chance to eat the dumplings. What is this speed, in rad/s?

(a) Estimate the terminal speed of a wooden sphere (density 0.870 g/cm3) falling through air, if its radius is 8.00 cm and its drag coefficient is 0.500. (The density of air is 1.20 kg/m3.)

Incorrect: Your answer is incorrect.

Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m/s

(b) From what height would a freely falling object reach this speed in the absence of air resistance?

Incorrect: Your answer is incorrect.

A large wrecking ball is used to destroy an old building. The operator uses a maximum angle of 6.0 ◦ . When the ball is at maximum amplitude, he starts timing the motion. He realizes that a full cycle and find that it lasts 7 s.

a. How long is the chain that holds the wrecking ball?

b. Find s(t) or θ(t).

c. Find θ such that the potential and kinetic energies are equal.

d. Had the operator used the same chain on the moon, would you expect the period to be larger or shorter? Explain.

e. The engineer in charge of the site thinks each cycle takes too long, so he asks the operator to use a lighter ball. What do you think about this?

Two metal rods, one silver and the other gold, are attached to each other. The free end of the silver rod is connected to a steam chamber, with a temperature of 100°C, and the free end of the gold rod to an ice water bath, with a temperature of 0°C. The rods are 5.0 cm long and have a square cross-section, 2.0 cm on a side. How much heat flows through the two rods in 60 s? The thermal conductivity of silver is 417 W/(m·K), and that of gold is 291 W/(m·K). No heat is exchanged between the rods and the surroundings, except at the ends.

A projectile is shot directly away from Earth's surface. Neglect the rotation of the Earth. What multiple of Earth's radius RE gives the radial distance (from the Earth's center) the projectile reaches if (a) its initial speed is 0.440 of the escape speed from Earth and (b) its initial kinetic energy is 0.440 of the kinetic energy required to escape Earth? (Give your answers as unitless numbers.) (c) What is the least initial mechanical energy required at launch if the projectile is to escape Earth?

1. A 4500 kg ore car accelerates at 0.4 m/s² up a ramp which has a 9 % grade. If the coefficient of friction µ_k = 0.25, calculate the force applied on the ore car. (4 points)

please type your answer, Please do not write on the paper and post it

A block of mass m1 = 4.15 kg is released from circled A. It makes a head-on elastic collision at circled B with a block of mass m2 = 10.5 kg that is initially at rest. Calculate the maximum height to which m1 rises after the collision.

Two 13-cm-diameter electrodes 0.56 cm apart form a parallel-plate capacitor. The electrodes are attached by metal wires to the terminals of a 11 Vbattery. After a long time, the capacitor is disconnected from the battery but is not discharged. What are the 1-----

a) charge on each electrode, b) the electric field strength inside the capacitor, and c) the potential difference between the electrodes right after the battery is disconnected?

2-----

What are a) the charge on each electrode, b) the electric field strength inside the capacitor, and c) the potential difference between the electrodes after insulating handles are used to pull the electrodes away from each other until they are 1.1 cm apart?

3-------

What are a) the charge on each electrode, b) the electric field strength inside the capacitor, and c) the potential difference between the electrodes after the original electrodes (not the modified electrodes of parts D-F) are expanded until they are 26 cm in diameter?

Question 4

An interesting topic in fluid mechanics is Bernoulli's equation, which relates pressures and velocities of a fluid with the density of rho at different heights, eq. 13.12. It has applications in the airspace. It can be used to measure flow speed in a pipe with a device named the Venturi meter (see figure 13.34). If the cross sections are 21 cm2 and 13 cm2, and the height difference resulted from the pressure difference is 0.2 m, calculate the speed of the flow in the pipe, v1 . Give your answer to one decimal point. Your Answer:Question 4 options:

Answer units