part a) When a 5.0-μF capacitor is connected to a generator whose rms output is 31 V, the current in the circuit is observed to be 0.25 A. What is the frequency of the source? (answer must be in Hz)

part b) An inductor has a 58.4-Ω reactance when connected to a 60.0-Hz source. The inductor is removed and then connected to a 47.0-Hz source that produces a 115-V rms voltage. What is the maximum current in the inductor? (answer must be in A)

part c) A sinusoidal voltage

Δv = (50.0 V)sin(180t)

is applied to a series RLC circuit with

L = 50.0 mH,

C = 170.0 μF,

and

R = 50.0 Ω.

(a) What is the impedance of the circuit in Ω?

(b) What is the maximum current in the circuit in A?

In the Bohr model, the Paschen series of spectral lines is caused by radiation absorbed or emitted as an electron transitions between the 2nd excited state and any higher excited state (3rd excited state and higher) of the hydrogen atom. The Paschen series spectral lines all involve infrared photons.

a) Using the Bohr model, calculate the energy of the electron when it is in the 2nd excited state, in units of electron-Volts (eV).

b) Calculate the energy of the electron when it is in the 3rd excited state, in units of eV.

c) Calculate the energy difference between the 2nd and 3rd excited states, in units of eV.

d) Suppose the electron falls from the 3rd excited state to the 2nd excited state. Calculate the wavelength of the radiation that is emitted in this transition. This is known as the Paschen alpha spectral line.

A motorcycle is following a car that is traveling at constant speed on a straight highway. Initially, the car and the motorcycle are both traveling at the same speed of 21.0 m/s , and the distance between them is 60.0 m . After t1 = 4.00 s , the motorcycle starts to accelerate at a rate of 7.00 m/s2 . The motorcycle catches up with the car at some time t2.

B) How long does it take from the moment when the motorcycle starts to accelerate until it catches up with the car? In other words, find t2−t1.

C) How far does the motorcycle travel from the moment it starts to accelerate (at time t1) until it catches up with the car (at time t2)? Should you need to use an answer from a previous part, make sure you use the unrounded value.

A see-saw made from 4 meter board sits on a pivot at its center. A child weighing 280 N sits 1.75 m away from the center. A second child who weighs 330 N sits on the other side such that the board remains horizontal and steady.

Now you come and push on the end of the seesaw nearest the second child with a force of 110 N. You don’t push straight up, but at an angle of 25° from the vertical – tilted a bit toward the center of the seesaw. The first child moves to maintain equilibrium.

(d) Based on your intuition, which way should the child move? Towards or away from the center?

(e) Calculate how far she is now from the center?

(f) What is the force now (magnitude and direction) that the pivot applies to the board?

1. An 8kg mass is observed traveling with a speed of .08*c.

What is its classical momentum?

What is the relativisitic momentum?

What is the difference between the two values?

Repeat the problem for a speed of .2*c and .8*c

If you travel by starship to the center of the galaxy such that you arrive within a subjective human lifespan, how much radiation damage will you suffer from the interstellar vacuum?

Assume special relativity holds and ignore the problems of accelerating and decelerating the spacecraft.

At what point in the journey through the interstellar vacuum would you will suffer too much radiation damage to go on?

How did you determine the amount of radiation damage? What equations did you need? What values did you use for the variables? How did you determine those values?

Hector read that the traditional drink in Tibet is tea with added butter. Inspired by this idea, he decides to investigate how a thin layer of fat on the top of a hot liquid affects the cooling of the liquid. He performs two different experiments.
Experiment 1: Hector pours 100 ml of boiling water into each of two Styrofoam cups and adds a thin (2.0-mm) layer of hot oil (at about 100∘C ) to one of the cups. He measures the initial temperature in the cups, waits for 10 minutes, and then measures the temperature again. His measurements are shown below.

Experiment 2: Hector puts two empty Styrofoam cups on separate precision scales and zeroes the scales. Then he pours 100 ml of boiling water into each cup and adds a 2.0-mm layer of hot oil to one of the cups. He records the initial readings of the scales, waits for 10 minutes, and then records the readings of the scales again. His data are shown below.

The surface area of the water in the cups is 3.0×10−3m2.

Part F

What other quantities relevant to the investigation can be determined or estimated from Hector's data?

a) The density of water

b) The number of moles of water

c) The rate of evaporation of oil

d) The density of oil

Two cars collide at an intersection. Car A, with a mass of 2000 kg , is going from west to east, while car B, of mass 1300 kg , is going from north to south at 17.0 m/s . As a result of this collision, the two cars become enmeshed and move as one afterwards. In your role as an expert witness, you inspect the scene and determine that, after the collision, the enmeshed cars moved at an angle of 65.0 ∘ south of east from the point of impact.

Part A: How fast were the enmeshed cars moving just after the collision?

v=_____________m/s

Part B: How fast was car AA going just before the collision?

Va=_____________m/s

A +7.50 μC point charge is sitting at the origin.

What is the radial distance between the 500 V equipotential surface and the 1000 V surface?

What is the distance between the 1000 V surface and the 1500 V surface?

Who discovered that thunderstorms give out electricity? Can you explain this process scientifically?

Which of the following statements are true for an atom with 3 energy levels? You can choose more than one answer.

When atomic electrons are excited to a higher level, they always return to their lowest energy level by jumping down one level at a time.

For a given battery voltage the kinetic energy of the free electron at the point of collision is higher if the atom is closer to the source of electrons.

When a free electron hits an atom, the atom is always excited to the highest energy level possible.

For a given position of the atom, the kinetic energy of a free electron at the point of collision increases as the voltage of the battery increases.

The number of different wavelengths emitted by the atom depends on the number of free electrons passing through the lamp.

The number of different wavelengths emitted by the atom depends on how much kinetic energy the free electron has when it hits the atom.

Photons are emitted as electrons in the atom jump up in energy.

In an inkjet printer, letters and images are created by squirting drops of ink horizontally at a sheet of paper from a rapidly moving nozzle. The pattern on the paper is controlled by an electrostatic valve that determines at each nozzle position whether ink is squirted onto the paper or not.

The ink drops have a mass \(\texttip{m}{m}\) = 1.00

A point charge 4.20 μC is held fixed at the origin. A second point charge 1.40 μC with mass of 2.80×10−4 kg is placed on the x axis, 0.260 m from the origin.

Part A: What is the electric potential energy U of the pair of charges? (Take U to be zero when the charges have infinite separation.)

Part B: The second point charge is released from rest. What is its speed when its distance from the origin is 0.600 mm?

Part C: What is its speed when its distance from the origin is 6.00 mm?

Part D: What is its speed when its distance from the origin is 60.0 mm?