A uniform hoop of mass M and radius R rolls down an incline without slipping, starting from rest. The angle of inclination of the incline is θ.

a. After moving a distance L along the incline, what is the angular speed ω of the hoop?

b. If the coefficient of static friction between the hoop and the incline is µs = 1/3, what is the greatest possible value of θ such that no slipping occurs between the hoop and the incline?

c. What is the direction of the angular velocity for the rolling hoop?

Using a coil of wire and an oscilloscope, explain how you can detect the presence of the Earth's magnetic field.

Using a coil of wire and an oscilloscope, explain how you could show that a magnet is producing a magnetic field.

A series LRC circuit is driven at a frequency which is much less than the resonant frequency with a sine wave voltage source V0sin(wt). What is the approximate voltage across the capacitor? Briefly explain

A series LRC circuit is driven at resonance with a sine wave voltage source. What is the sum of the voltages across the inductor and the capacitor in an ideal circuit? Briefly explain.

2. For a system of non-interacting, one-dimensional, distinguishable classical particles in a harmonic oscillator potential, V = kx² in contact with a particle reservoir with chemical potential µ and a thermal reservoir at temperature T.

(a) Calculate the grand partition function Z for the system. Note that there is no fixed "volume" for this system.

(b) Obtain N (number of particles) and U as functions of µ and T and show that U satisfies the equipartition theorem

A 3.4 μC charge is placed at the origin of coordinates, and a -2.6 μC charge is placed to the x axis at 5.0 cm . 1)Find the location of the place(s) along the x axis where the electric field due to these two charges is zero. Express your answer(s) using two significant figures. If there is more than one answer, enter each answer separated by a comma. 2)Find the location of the place(s) along the x axis where the electric potential due to these two charges is zero. Express your answer(s) using two significant figures. If there is more than one answer, enter each answer separated by a comma?

- estimate the energy (in joule) produced from radioactivity over the Earth's lifetime.

- Estimate the energy density (in joule/kg) of nuclear fission fuels.

- Estimate mass (in kg) of radioactive material is need to power Earth’s interior over its lifetime.

- Estimate the mass of Earth (in kg).

- Estimate the fraction of Earth's mass in radioactive material.

Consider the 1D wave equation d^2u/dt^2 = c^2( d^2u/dx^2) with the following boundary conditions: u(0, t) = ux (L, t) = 0 . (a) Use separation of variables technique to calculate the eigenvalues, eigenfunctions and general solution. (b) Now, assume L = π and c = 1. With initial conditions u(x, 0) = 0 and ut(x, 0) = 1, calculate the solution for u(x, t). (c) With initial conditions u(x, 0) = sin(x/2) and ut(x, 0) = 2 sin(x/2) − 3 sin(5x/2) calculate the solution for u(x, t).

A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The generator voltage varies in time as ε =V_a - V_b = ε_msinωt, where ε_m = 120 V and ω = 231 radians/second. The inductance L = 155 mH. The values for the capacitance C and the resistance R are unkown. What is known is that the current in the circuit leads the voltage across the generator by φ = 49 degrees and the average power delivered to the circuit by the generator is P_avg = 106 W.

What is I_max, the amplitude of the current oscillations in the circuit?

What is R, the value of the resistance of the circuit?

What is C, the value of the capacitance of the circuit?

The value of ω is now changed, keeping all other circuit parameters constant, until resonance is reached. How was ω changed?

ω was decreased

ω was increased

What is the average power delivered to the circuit when it is in resonance?

Four identical charges (+2.0 ?C each) are brought from infinity and fixed to a straight line. The charges are located 0.40 m apart. Calculate the amount of work done in assembling the charges.

1) What are a Vande Graaf generator and a Tesla Coil? Why aren’t people hurt when they come in contact with such high voltage?

2) What is the difference between AC and DC? Three prong and two prong plugs? 110 and 220 plugs?

A 2.25×10⁴ N elevator is to be accelerated upward by connecting it to a counterweight using a light (but strong!) cable passing over a solid uniform disk-shaped pulley. There is no appreciable friction at the axle of the pulley, but its mass is 875 kg and it is 1.50 m in diameter.

How heavy should the counterweight be so that it will accelerate the elevator upward through 6.00 m in the first 4.00 s , starting from rest?

Under these conditions, what is the tension in the cable on elevator side of the pulley?

Under these conditions, what is the tension in the cable on counterweight side of the pulley?

I posted this before but 3000 wasnt the correct answer

Three point charges are arranged as follows: Charge Q1 = + 5.00 nC is located at the origin. Charge Q2 = -3.00 nC is located at x = +4.00 cm, y = 0 cm. Charge Q3 = + 6.00 nC is at x = 0 cm, y = -3.00 cm. a. What is the net electric field at point P with coordinates x = 4.00 cm, y = -3.00 cm?

(i) Express your answer as a vector in i, j, k notation.

(ii) Express your answer as the total magnitude and direction θ from the +x-axis. b. What is the net electric force on an proton placed at point P? Express your answer only in terms of magnitude and direction.

c. What is the acceleration of this proton? Express your answer only in terms of magnitude and direction. Mass of the proton is 1.673∙10-27 kg.

What starts a dislocation and how does this advance in a crystal structure?

This question is about throwing a ball vertically upwards and catching the ball.

Compare the part of the graph of mechanical energy vs. time before the ball is in free-fall to the part while the ball is in free fall. Carefully explain, using the concept of work done on the system, why the ball’s mechanical energy changed as it did.