A rock sample is placed in a strength-testing machine at atmospheric pressure and is compressed axially to failure. A force of 12,000 Ibf was required for rock failure, and the cross- sectional area of the sample were 2.0 sq in. The sample failed along a plane that marks a 35 angle with the direction of compressional loading A) Construct the Mohr's circle using the two principal stresses present B) Compute the shear stress present along the plane of failure C) Compute the normal stress to the plane of failure. D) Compute the angle of internal friction. E) Compute the cohesive resistance of the material. F)Label the parameters computed in the previous four steps on the Mohr's circle construction. Using the Mohr criterion, compute the compressional force required for rock failure if the sample is placed under a 5,000-psi confining pressure.

a Ball is thrown upward from the top of a 23.5 m building with a speed of 12.4 m/s. ignore air resistance

A) draw and label a figure with a coordinate system showing the balls initial position and initial velocity.

B) write down the proper equations of motion and replace all known initial conditions and constant values with their appropriate numerical values to find the following

C)to what maximum height above the ground will the ball rise?

D) how much time does it take the ball to reach this maximum height?

E) what is the acceleration of the ball when it reaches this highest point?

F) How much time does it take the ball to fall from the top to the ground?

G) With what speed does the ball hit the ground?

H) With what velocity does the ball hit the ground?

. Light travels at different speeds through materials due the refractive index of that material. Given that I have a transparent polymer material, would light travel faster or slower through it if it (a) have zero stress on it or (b) have a substantial, but still elastic, stress on it (say 20 MPa for HDPE)? Explain.

In radiation safety classes, it is stressed that the amount of radiation that a person receives is to be ALARA (As Low As Reasonably Achievable). Explain how distance, shielding and time meet this goal.

1.As a result of any natural process, the total entropy of any system plus that of its environment As a result of any natural process, the total entropy of any system plus that of its environment?

A) always stays the same. B) sometimes decreases. C) never decreases. D) never increases.

2.According to the second law of thermodynamics, the entropy of any system always increases. According to the second law of thermodynamics, the entropy of any system always increases.

A)True B)False

3. An ice cube at 0°C is placed in a very large bathtub filled with water at 30°C and allowed to melt, causing no appreciable change in the temperature of the bath water. Which one of the following statements is true?

A)The entropy of the system (ice plus water) increases because the process is irreversible.

B)The entropy lost by the ice cube is equal to the entropy gained by the water.

C)The net entropy change of the system (ice plus water) is zero because no heat was added to the system. D)The entropy gained by the ice cube is equal to the entropy lost by the water.

E)The entropy of the water does not change because its temperature did not change.

4.An engine manufacturer makes the claim that the engine they have developed will, on each cycle, take 100J of heat out of boiling water at 100∘C, do mechanical work of 80J, and exhaust 20J of heat at 10∘C. What, if anything, is wrong with this claim?

A)There is nothing wrong with this claim because 100J=20J +80 J.

B)An engine would operate by taking in heat at the lower temperature and exhausting heat at the higher temperature.

C)The efficiency of this engine is greater than the ideal Carnot cycle efficiency.

D)This engine violates the first law of thermodynamics because 100 J +20J ≠ 80 J.

E)The heat exhausted must always be greater than the work done according to the second law of thermodynamics.

Describe the process of “magnetic cooling” (adiabatic demagnetization) for a paramagnetic salt in words (how and why does it work?).

Illustrate this process in an entropy - temperature diagram.

Describe the formation and travel direction (and why) of a North Atlantic hurricane that might impact North America

Heat flows from a reservoir at 373 K to a reservoir at 273 K through a 0.39-m copper [thermal conductivity 390 J/(s

Newton’s Law of Motion

Part 2 data: Tilted Track

(PLEASE SHOW ALL WORK)

1. Draw four FBD (free body diagrams) with Fnet vectors for the following four cases. (Neglect friction and drag.) (Define coordinate systems for each object, where each coordinate system is aligned with the object’s acceleration.)

a. Hanging mass while accelerating down (b). Cart on flat track while accelerating (from part 1 data)

c. Cart on inclined track while accelerating (d). Cart on declined track while accelerating (this is from part 2 data)

2. For case 1a above, write out Newton’s 2nd Law in the y-direction and solve for the tension: TH.

3. For cases 1b, 1c, and 1d, write out Newton’s 2nd Law in the x-direction and solve for the tension: TC.

4. Start an Excel data table and organize all your data (angles, mC, mH, and cart accelerations)

5. Nearby, start an Excel results table. Here, calculate the following quantities once per trial.

Reminder: If you use sine or cosine in MS Excel, it expects the angle to be entered in radians. You can input degrees by using “sin(radians(A1))” and “cos(radians(A1))”.    (Change “A1” to match your angle’s location.)

a. the net force acting on the cart, using Fnet=ma.

b. the net force acting on the hanging mass, using Fnet=ma.

c. the tension force, TH, acting on mH.

d. the tension force, TC, acting on mC. Do not use the tension value from part c!

e. the fraction TC/TH.     (What should this ratio be if your data was perfect?)

6. For your TC/TH values, calculate the average, standard deviation, and percent error between your average and the accepted value.

7. Make a single scatter plot showing the cart’s acceleration vs. the net force on the cart. Use three data series: 1) first four trials, 2) heavy cart, and 3) tilted track.

8. Add a linear trend line to each data set. For each trend line, use “Set Intercept” with a value of zero. Display the equation for each trend line.   (When the net force is zero, the acceleration had better be zero. Thus, the y-intercept should be 0 m/s2.)

A parallel plate capacitor with adjustible plate separation d and adjustible area A is connected to a battery. The capacitor is fully charged to Q Coulombs and a voltage of V Volts. (C is the capacitance and U is the stored energy.) Give all correct answers concerning a parallel-plate capacitor charged by a battery (e.g. B, AC, CDF).

A) After being disconnected from the battery, increasing the area A will increase C.
B) With the capacitor connected to the battery, increasing the area A will decrease U.
C) With the capacitor connected to the battery, increasing d increases U.
D) With the capacitor connected to the battery, increasing the area A will increase Q.
E) After being disconnected from the battery, increasing d increases V.
F) With the capacitor connected to the battery, increasing d increases C.

(Show all the steps please)

Rotational Dynamics: Four objects of equal mass start at the top of an inclined plane. A solid cylinder, a thin walled cylinder, a solid sphere, and a thin walled sphere. All objects start at rest. Starting at rest,

A) Write down the work energy theorem including both kinetic energy terms and all potential energy terms.

B) If all four objects are released at the same moment, how long does each take to reach the bottom of the incline plane?

C) Find the ratio of translational (linear) kinetic energy to rotational kinetic energy for each object.

D) Compare the results of the race obtained in part a to the results obtained in part b.

E) If the ramp is 20 m long and inclined at an angle od 20 degrees, what is the angular speed of the solid cylinder at the bottom of the ramp.

F) What torque is required to achieve this final angular speed?

(1) Imagine that we have an electron traveling due west from the capitol of the united states steps. It is traveling at 98.94% of the speed of light.

(a) What is the force on the electron from the magnetic field?

(b) What is the radius of curvature of the path that it follows?

(c) What would the answers to parts (a)-(c) be for a proton?

A 6.61-mm-high firefly sits on the axis of, and 14.1 cm in front of, the thin lens A, whose focal length is 5.21 cm. Behind lens A there is another thin lens, lens B, with focal length 21.1 cm. The two lenses share a common axis and are 60.3 cm apart. Is the image of the firefly that lens B forms real or virtual?

How far from lens B is this image located (expressed as a positive number)?

What is the height of this image (as a positive number)? Is this image upright or inverted with respect to the firefly?

A 175 g mass attached to a horizontal spring oscillates at a frequency of 2.80 Hz. At t =0s, the mass is at x= 7.00 cm and has vx =− 35.0 cm/s . Determine:

The maximum speed.

The maximum acceleration.

The total energy.

The position at t= 2.80 s .

In the previous parts, the following was found: period = 0.357 s, angular frequency = 17.59 rad/s, amplitude = 7.277 cm, phase constant = 15.8679 degrees.

Fluid Mechanics: A water tank is a cylinder 4 m in height and 2 meters in diameter. The tank is full at time t_o. The tank sits on a platform 12 m tall. A water tap is located at the bottom center of the tank. The tap, when actuated, opens to a pipe 5 cm in radius.

a.       Write down Bernoulli’s equation. Identify the Pressure, Kinetic and Potential Energy terms. Show that each has the units of an energy density (Joules/Volume).

b.       Use Bernoulli’s equation to compare the difference in pressure between the surface of the water and the bottom of the tank near the edge? Assume the fluid is motionless near the edge.

c.       When a tap is opened water rushes in to a pipe 5 cm in radius. The pipe is straight and drops 12 m to ground level, but along the way slowly in radius to 2 cm. What is the speed of the water as it emerges from the pipe?

d.       Use the continuity equation to find the speed of the water as it enters the pipe 12 m above, i.e. bottom of the tank.

e.       What is the volume and mass flow rate of the stream of water?

f.        What is the pressure of the fluid as it enters the pipe, again at the bottom of the tank.