A regular icosahedron, as shown in the figure, has an outer radius (defined as the distance from the centre to a vertex) of 9.51 cm and an inner radius (defined as the distance from the centre to the centre of a face) of 7.56 cm. It has 20 faces which are equilateral triangles with side length 10.0 cm, and 12 vertices.
Twelve negative charges of magnitude 20.0 μC are placed at the vertices and 20 positive charges of magnitude 12.0 μC are placed at the face centres. A positive charge of Q = +44.25 μC is placed at the centre of the icosahedron.

1. What is the force acting on the charge at the centre of the icosahedron? [1]

2. If one of the negative charges at a vertex is removed, what is the force on the charge at the centre of the icosahedron? [2]

3. If one of the positive charges at the face is removed, what is the force on the charge at the centre of the icosahedron? [2]

4. Using your answers to parts ii) and iii) what is the net force on the charge Q at the centre if a complete face (i.e. one positive charge and the three surrounding negative charges), is removed? [5]

Protons having a kinetic energy of 5.00 MeV (1 eV = 1.60 x 10-19 J) are moving in the positive x direction and enter a magnetic field B = 0.025 T directed out of the plane of the page and extending from x = 0 to x = 1.00 m as shown in the Figure below. (a) Ignoring relativistic effects, find the angle α between the initial velocity vector of the proton beam and the velocity vector after the beam emerges from the field. (b) Calculate the y component of the protons’ momenta as they leave the magnetic field.

When we say that momentum is conserved for an isolated system, what specifically does that mean?

The photogates in the experiment are used to determine the speed of the gliders passing through. The photogates measure the time it takes for the photogate beam to go from being unblocked to blocked to unblocked again. You tell the photogate how long your glider is, and the speed is then calculated.

Given the description of what the photogates do, how will you determine the velocity of the glider?

A 7.50-kg box slides up a 25.0o ramp with an initial speed of 7.50 m/s. The coefficient of kinetic friction between the box and ramp is 0.333. You wish to calculate the distance the box will move up the ramp before coming to a stop using mechanical-energy (NOT force-motion or the work-kinetic energy.)

a. Write the correct equation for solving the problem, and then fully justify its use. (Start by identifying the objects in the system [only the required objects] and then proceeding as in class.)

b. Beginning with the equation in (a), calculate the desired distance.

c. Calculate the change in the thermal energy of the system as the box moves from the bottom of the ramp to where it stops.

1. Describe how bremsstrahlung and characteristic x-rays are created. Why are there no characteristic x-rays created under 70 kVp? Be thorough in your answer and cover each step in the process (2 points).

2. Which x-ray interaction with tissue involves ejecting an inner shell electron? Which tissue interaction is the major source of technologist dose? (1 point)

3Objectives•To determine the relationship between kinetic, potential, and total mechanical energy for a cart on an incline.•To determine the work done by friction on a sliding cart.•To show that energy is not conserved when a non-conservative force, like friction, is acting.Procedure: Energy of a cart withoutf riction In this experiment, we will assume that friction is negligible, and that there are no non-conservative forces at work.The motion of a cart rolling down an incline will be examined using real-time velocity and position values from a motion sensor. Examining the position and velocity of the cart as it rolls down the track allows us to also determine the energy of the cart. In this experiment you will examine the transition between gravitation potential energy and kinetic energy as the cart rolls down an incline.1.Figure 1 was set up in real time, where the ramp was inclined at an angle of 8.5°, and the mass of the cart is 0.250 kg. A Motion Detector was attached to the upper end of the track.As the cart slides down the track, the motion detector ispre-programmed to measure the distance (position) of the cart from the bottom of the ramp –see (d) infigure 1.2.Gravitational potential energy depends on position, and kinetic energy depends on velocity. The cart was released,and the position and velocity of the cart were measured with the motion sensor software. Time(seconds)Position(meters)Velocity(meters/second )

0.866658 1.273902 0.265542

0.899991 1.256238 0.471058

0.933324 1.239259 0.557238

0.966657 1.219022 0.618978

0.99999 1.197756 0.667428

1.033323 1.174775 0.720021

1.066656 1.14905 0.752035

1.099989 1.124183 0.771615

1.133322 1.098115 0.802199

1.166655 1.070846 0.8365

1.199988 1.042034 0.866512

1.233321 1.013222 0.901099

1.266654 0.982867 0.959695

1.299987 0.948738 1.006286

1.33332 0.915639   1.046589

1.366653 0.878766 1.080032

1.399986 0.842923 1.094753

1.433319 0.806908 1.141773

1.466652 0.766777 1.191794

1.499985 0.728361 1.266254

1.533318 0.682056 1.33071
43.Now, it’s time to plot the PE, KE, and total ME of the cart as it rolls down the track.To do this, let’s first convert each position, d, to a height so we can calculate the potential energy of the cart. Open the data above in excel and create a new column labeled height. Using equation 7,convert every position measurement to the vertical height of the cart. In excel, make sure you use 0.1500983 (radians) for your angle, θ,Instead of 8.5°(degrees).

4.Create another new column titled Kinetic Energy. Create a formula which grabs each velocity value and, using your measured mass, calculates the kinetic energy of the cart(equation1).

5.Next, create another new column that calculates Gravitational Potential Energy as the cart rolls down the incline. Create a formula which multiplies the height by the mass of the cart and gravitational acceleration(equation 2).

6.Finally, create a third new column titled Mechanical Energy, which is just be the sum of your two columns, Kinetic Energy and Gravitational Kinetic Energy.

7.Create a line graph of kinetic energy versus time, potential energy versus time,and mechanical energy vs time on the same graph. Under your graph options, be sure to show a legend, so whoever reads your report will have no trouble determining which line is which.Attach the graph with your lab submission.

8.What is the approximately slope of your kinetic energy graph? What does this suggest about your cart’s kinetic energy as a function of time?

9.What is the approximately slope of your potential energy graph? What does this suggest about your cart’s kinetic energy as a function of time?
10.Analyze your graph carefully. What is the approximate slope of your mechanical energy graph? What does this suggest about your cart’s total mechanical energy?

Refer to the illustration below. Light enters the stacked transparent plates at an angle of from the normal at location zero cm in the x direction.

• Identify the refraction angle from the normal at each medium change interface.
• Identify the displacement of the exit beam (in the x direction) from the entrance location.

for materials class

Manipulating strength

a. Using words and visuals, briefly describe 4 strategies to increase the strength of a metal.

b. What do these strategies have in common in terms of their mechanism?

c. Use a plot to discuss the trade-off between strength and ductility in metals. Explain why this trade off occurs based on the mechanism of plastic deformation in metals.

5 rems per year whole body occupational dose is the generally agreed limit by the standard setting bodies. State your opinions on this limit; do you agree with it?

A small meteorite (30 kg) is falling through the earth’s atmosphere. It is moving very fast - in fact, faster than the terminal velocity it would have reached if had been dropped from a great height. In a situation like this, the drag force is stronger than the weight. At one moment, the magnitude of the meteorite’s acceleration is 4.0 m/s². You need to calculate the magnitude of the drag force on the meteorite.

1. Draw a free-body diagram, which includes an arrow for each individual force on      the meteorite (and labels to indicate the type of force), an arrow for the net force,      and a coordinate system.     

2. In this situation, the velocity of the meteorite and the acceleration of the meteorite point in [the same direction, in opposite directions].

3. In this situation, the velocity of the meteorite and the net force on the meteorite      point in [the same direction, in opposite directions].

4. In this situation, the magnitude of the drag force on the meteorite is [increasing,      decreasing, remailing constant].

5. Write an algebraic expression that shows how the individual forces combine to      produce the net force on the meteorite. The signs in the expression must be

              consistent with the coordinate system in the free-body diagram. (That is, add in      all the forces in the positive direction and subtract all the forces in the negative      direction.)

6. Set that expression equal to ma and solve the resulting equation for the

              magnitude of the drag force. Type out the equation with all known numbers      inserted in their proper places and then just state the answer.

.

A cannonball is fired at a cliff 1000 m away and strikes it 250 m above the level ground 5 seconds later.

a. What is the angle (in degrees) with which the cannonball was fired, with respect to the level ground? (g = 10 m/s²)

b. What was the approximate initial speed (in m/s) with which the cannonball was fired? (g = 10 m/s²)

c. Which time (in seconds) below is the closest to the time after firing that the cannonball reaches (or would reach) maximum height? (g = 10 m/s²)

Big Ben in London is the most accurate mechanical clock of its size. The 300-kg hour hand is 2.7 m long, and the 100-kg minute hand is 4.2 m long. Treat each hand as if it were a thin rod. Calculate the rotational kinetic energy of the two-hand system.

Derive the Jones matrix of a liquid crystal cell?

Why can gravitational potential energy be ignored in a verticle spring with a hanging mass? My TA mentioned something about no work being done by GPE, but that doesn't really make sense. Also, the assignment is asking for it to be explained conceptually, not with equations. Thanks!