A circular saw blade (E = 200 GPa, v = 0,3) can be considered as a 2 mm thick disc with an outer diameter of 600 mm and central hole of 100 mm diameter bolted to a rigid inner rotating disc. Determine the maximum rotational speed if initial yielding of the disc occurs for a Tresca yield stress of 200 MPa.

A bottle of mass mb =0.1 kg and volume V =0.1m3 is attached to the bottom of a vertical thin rod of length l = 1 m and mass mr = 2 kg, that is hinged at the top end. The bottle is full of hydrogen (mH = 1.67 × 10−27 kg) and is at atmospheric pressure and temperature T0 = 20 0C.

(a) What are the number of moles and the initial rms velocity of the hydrogen?

(b) The temperature of the oxygen in the bottle is now increased to T = 100 0C. What is the new pressure inside the bottle?

(c) At this temperature, the cork at the end of the bottle, mass mc = 0.05 kg and cross- sectional area A = 0.01 m2, pops off causing the cork to fly off in one direction (as- sumed to be in the horizontal direction). If the cork was held in by a kinetic friction fk =100N,andittakes∆t=0.01sforthecorktopopoff,whatisthespeedofthe cork as it flies off? (Hint: Use impulse.)

(d) While the cork is flying off, what must be conserved? Be specific. After the cork flies off, the rod/bottle system begins to swing with an angular speed of ω. Determine ω for the rod/bottle system. (You may ignore the mass of the air inside the bottle.)

(e) To what height will the rod/bottle system swing up to? (Hint: Don’t forget about the center of mass of the rod.)

Write an expression for the instantaneous voltage ?(?) delivered by an ac generator supplying 120 V rms at 70 Hz. Assume the voltage is 0 at time ?=0, and leave the factors in exact form; do not round their values. Write the argument of the sinusoidal function to have units of radians, but omit the units.

2. Assume that the potential in Cartesian coordinates is given as V=x²-y². According to this;

(a) The value of the potential at coordinate P (2, -1,3)

(b) Electric field, the magnitude of the displacement vector and field lines

(c) Calculate the charge density on the conductive surface

1- A 9 V battery is powering a simple circuit with one light bulb. There is a current of 0.58 running through the bulb and a voltage drop of 5.8 across the bulb. What is the internal resistance of the battery?

2- A series circuit uses three resistors. One resistor has a resistance of 19 Ω. The second resistor has a resistance of 26 Ω. The final resistor has a resistance of 21 Ω. What is the equivalent resistance of this circuit?

3- A parallel circuit consists of two resistors in parallel. The first resistor has a resistance of 17 Ω and the second resistor has a resistance of 57 Ω.  What is the equivalent resistance of this circuit?

4- Which of the following are true about using an ammeter in a circuit?

4- in a _____________ circuit, the components are connected in a single line. If more resistors are added to this circuit, then total current _________ and the equivalent resistance ___________ compared to the original circuit. in a __________ circuit, the components are connected in branches. If more resistors are added to this circuit, then the total current ____________ and the equivalent resistance ____________ compared to the original circuit.

options: series, decreases, remains unchanged, parallel, incomplete, increases

1. If you connect a 9 v battery up to a 7 Ω resistor and a 10 μF capacitor for a very long time, what would the current in the circuit be?

2. What is the time constant in an RC circuit and how is it found?

3. In your own words what is meant by an RC circuit and give an example of one you might find in the real world.

For the following u(x, y), show that it is harmonic and then find a corresponding v(x, y) such that f(z)=u+iv is analytic.

u(x, y)=(x^2-y^2) cos(y)e^x-2xysin(y)ex

Near the surface of the Earth there is an electric field of about 150 V/m which points downward. Two identical balls with mass 0.407kg are dropped from a height of 2.29m , but one of the balls is positively charged with q1 = 338?C , and the second is negatively charged with q2=-338?C . Use conservation of energy to determine the difference in the speeds of the two balls when they hit the ground. (Neglect air resistance.)

In Griswold v. Connecticut, the U.S. Supreme Court stated that “specific guarantees in the Bill of Rights have penumbras, formed by emanations from those guarantees that help give them life and substance.”

1. Discuss the meaning and implications of Griswold’s penumbras and emanations

2. Describe the legal basis for an unenumerated right that might be located within these purported constitutional regions.

(a) Calculate the wavelength of an electron under an acceleration voltage of (i) 200 V, (ii) 1.5 MeV and (ii) 2.5 GeV. Also, calculate the velocity of electrons moving at these acceleration voltages. How does this velocity compare to the speed of light. If they are comparable to the speed of light, use relativistic effects to calculate the wavelength of electron?

(b) If the wavelengths are so small, can one expect the resolution of the TEM made with these energies to be so small? If not, what will be the reason behind those discrepancies.