What is kinetic energy and how does it relate to the Boltzmann distribution?

1. (a) Find the charge stored on each capacitor in Figure 18.24 (C₁ = 30.0 µF, C₂ = 4.50 µF) when a 1.51 V battery is connected to the combination.
C₁
___C?
C₂
___C?
0.300 µF capacitor
___C?

(b) What energy is stored in each capactitor?
C₁
___J?
C₂
___ J?
0.300 µF capacitor
____J ?

2.(a) What voltage must be applied to the 10.0 µF capacitor of a heart defibrillator to store 450 J in it?
____ kV ?
(b) Find the amount of stored charge.
___ C ?

A hydraulic jack is designed to lift a car by exerting an output force 100 times as large as the input (see class notes). (a) What must be the ratio of the cylinder diameter on the output side to that on the input side? (b) If the input side is pushed down by 10 cm, how much does the output side move up? (The fluid volume lost on the input side is gained on the output side.) (c) Show that the work we do on the input side equals the work done on the car on the output side (as it must), assuming no frictional losses.

A 0.042 kg aluminum bullet traveling at 456 m/s strikes an armor plate and comes to a stop. If all its energy is converted to heat that is absorbed by the bullet, what is the bullet's temperature change in degrees Celsius? (This is a multi-step problem.)

1a. An unidentified flying object (UFO) is observed to travel a total distance of 46000 m, starting and ending at rest, over a duration of 1.57 s. Assuming the UFO accelerated at a constant rate to the midpoint of its journey and then decelerated at a constant rate the rest of the way, what was the magnitude of its acceleration? Express your answer in g s , where 1 g = 9.81 m/s^2.

b. A Ford passes a Toyota on the road (both vehicles are traveling in the same direction). The Ford moves at a constant speed of 45.3 m/s. Just as the Ford passes it, the Toyota is traveling at 16.0 m/s. As soon as the Ford passes the Toyota, the Toyota begins to accelerate forward at a constant rate. Meanwhile the Ford just keeps going at a steady [] m/s to the east. The Toyota catches up to the Ford a distance of 89.0 m ahead of where the Ford first passed it. What was the magnitude of the Toyota s acceleration?

c. Driving down the road at a speed of 33.7 m/s, you suddenly notice a fallen tree blocking the road a distance of 85.1 m ahead of you. You step on the brake pedal and decelerate at a constant rate. What must the magnitude of your acceleration be so that you will come to a stop 5.4 m in front of the tree?

2 Pascal’s Principle
An Olympic swimming pool is 50 m long, 25 m wide, and 2 m deep.
(a) Make a plot of pressure as a function of depth in the pool, for 0 ≤ y ≤ 2 m.
(b) What is the pressure on the bottom of the pool?
(c) What is the total force on the bottom of the pool — the 25 m × 50 m surface?
(d) What is the total force on one end of the pool — one of the 25 m × 2 m surfaces?
(e) What is the total force on one side of the pool — one of the 50 m × 2 m surfaces?

The electron gun in a television tube uses a uniform electric field to accelerate electrons from rest to 4.7×10⁷ m/s in a distance of 1.3 cm .

What is the electric field strength?

The Second Edition of the Oxford English Dictionary is currently available as a 20-volume print edition and costs $895. Imagine that the publishers would like to distribute a lower-cost version of the dictionary that still contains all of the same words, but in a smaller number of volumes. To accomplish this, they decide to reduce the font size to 1/3 of the original font size and include a simple biconvex single-lens magnifier with the new reduced-volume set. (a) Fully specify a design for the required single lens magnifier. (b) If the publishers had wanted to severely reduce the font size to 1/15 of the original size, could they still supply a single-lens magnifier for the customers to use? Specify a design for such a magnifier and identify any physical and/or optical performance limitations that arise. What is the maximum diameter possible for this magnifying lens?

A satellite is in an elliptical orbit around the earth. The distance from the satellite to the center of the earth ranges from 7.2 Mm at perigee (where the speed is 8.0 km/s) to 9.9 Mm at apogee.

1. Assume the initial conditions are x = 0, y = 7.2 × 106 m, vx = 8.0×103 m/s, and vy = 0. Use python program to print its speed, distance from the earth, kinetic energy, potential energy, and total mechanical energy for each iteration. (What equations should I put in to the program?)

2. Is mechanical energy conserved?

ANSWER THE FOLLOWING QUESTION AND DRAW DIAGRAM FOR EACH PART OF QUESTION

Q1(A).Two point charges are located on the x axis. The first is a charge +Q at x = a. The second is an unknown charge located at x = -3a. The net electric field these charges produce at the origin has a magnitude of 2keQ/a2. What are the two possible values of the unknown charge?

Q1(B)In Fig. 3, particle 1 of charge +1 μC and particle 2 of charge -3.0 μC are held at
separation L =10.0 cm on an x axis. If particle 3 of unknown charge q3 is to be located such that the net
electrostatic force on it from particles 1 and 2 is zero, what must be the (a) x and (b) y coordinates of
particle 3?

Q1(C)In Fig. 2, two identical, electrically isolated conducting spheres A and B are separated
by a (center-to-center) distance ‘a’ that is large compared to the spheres. Sphere A has a positive charge
of ∆Q, and sphere B is electrically neutral. Initially, there is no electrostatic force between the spheres.
(The large separation means there is no induced charge.)
(a) Suppose the spheres are connected for a moment by a conducting wire. The wire is
thin enough so that any net charge on it is negligible. What is the electrostatic force
between the spheres after the wire is removed?
(b) Suppose sphere A is grounded momentarily, and then the ground connection is
removed. What now is the electrostatic force between the spheres?

the question on its own don't have any figures please do make diagrams where necessary for better understanding of answers

A uniform cylinder of radius 14 cm and mass 27 kg is mounted so as to rotate freely about a horizontal axis that is parallel to and 9.3 cm from the central longitudinal axis of the cylinder. (a) What is the rotational inertia of the cylinder about the axis of rotation? (b) If the cylinder is released from rest with its central longitudinal axis at the same height as the axis about which the cylinder rotates, what is the angular speed of the cylinder as it passes through its lowest position?

A 100 pF capacitor has circular plates of 10.0 cm radius that are 5.0 mm apart and have air beteween them. The capacitor is charged by connecting it to a 12.0 V battery through a 1.0 ohms resistor.

a) Determine the current through the plates at t = 0 (when the battery is connected)

b) Determine the current through the plates at t = 60s?

c) Determine the rate at which the electric field between the plates changes at t= 0 and t = 60s

d) Determine the magnetic field between the plates at t = 0 and at t = 60s

Don't really care about the answers as much, but more about what formulas are being used.

Thanks!

Two parallel conducting plates are oriented in an ? − ? coordinate system. The plates are separated by a distance ? = 0.05 ?, and the origin of the coordinate system is halfway between the plates. The plate separation is very small compared to the size of the plates. The left plate is at a potential ?_L = 50 ?, and the right plate is at a potential ?_R = 10 ?.

1. A proton at the origin begins at rest. Use conservation of energy to find its velocity when it hits one of the plates. Which plate does it hit?

2. An electron at the origin begins with an initial velocity ?⃗? = (4 × 106 ?/?)?̂. Use conservation of energy to find its velocity when it hits the right plate?

3. What is the acceleration of a proton at the origin? Express your answer in unit vector notation.

3. What is the acceleration of a proton at the origin? Express your answer in unit vector notation.

which of the following motions should be correctly analyzed using the torque version of Newton's 2nd law? Circle all that apply.

a. a car slows to a stop as it approaches a traffic light on a straight road.

b. a car travels around a circular path.

c. a car travels around a circular path on a banked road.

d. the tires of a car spin at a constant rate as the car goes around a curve.