k=9.00*10^9 Nm^2/C^2. Pay attention to unit conversions.

In one experiment the electric field is measured for points at distances r from a very long, straight line of charge that has a charge per unit length λ. In a second experiment, the electric field is measured for points at distances from the center of a uniformly charged insulating sphere that has total charge Q and radiusR = 8.00 mm. The results of the two measurements are listed in the table below, but you are not told which set of data applies to which experiment.

To solve the mystery, start by creating the graph ln(E) versus ln(r) for each data set. Make sure you convert r values to meters before calculating ln(r).

Use Excel. The axes should be labeled appropriately, and the graphs should be titled Measurement A and Measurement B, respectively. Show a linear trendline and its equation for each graph. Make sure that the numerical coefficients of the trendline equation show at least five significant digits, you will need them in your calculations below. You will submit the Excel file showing the graphs to Blackboard, separate from the test. (5 points)

Now answer the following questions:

1. a) Use these graphs to determine which data set, A or B, is for the uniform line of charge and which set is for the uniformly charged sphere. Explain your reasoning.

2. b) Use the trendline equation of the graph corresponding to the line of charge to calculate λ. Show neatly your calculations.

3. Use the trendline equation of the graph corresponding to the charged sphere to calculate Q. Show neatly your calculations.

4. Calculate the electric field inside the sphere, at 4.00 mm from the center. Show neatly your calculations.

Hint: If the electric field is invers proportional to a power of r, say E = B/rn with B a constant factor, then ln(E) = ln(B) - n∙ln(r). So, the graph of ln(E) versus ln(r) should be a straight line, for which the slope is -n and the vertical intercept is ln(B).
Now apply this idea to the electric field of a line of charge for which E = 2kλ/r, so ln(E) = ln(2kλ) - ln(r), and to the electric field outside of a uniformly charged sphere for which E = kQ/r , so ln(E) = ln(kQ) -2ln(r). What is left for you is to compare these theoretical equations to the trendline equations of the charts and identify which one applies best to Measurement A and which one to Measurement B.

1. Consider the following situation. With the power supply off, the current limit one-half of a turn and the voltage knob completely counterclockwise, a coil is connected to it. A secondary coil is placed just in front and connected it to a galvanometer. If you gently increase the voltage of power supply, explain what you would observe in the galvanometer. Would the needle deflect? Why?

2. If the secondary coil is moved away from the primary coil, would the deflection of the needle be larger, smaller, or the same? Explain!

3. In this experiment, you moved the bar magnet closer to or away from the coil while keeping the coil stationary. How would the result change if the moved the coil while the bar magnet is kept at rest? Explain!

If you move both the bar magnet and the coil, how would this motion change the result you observed in this experiment. Explain!

Two thin square flat sheets are placed parallel to each other. The distance between the sheets is much smaller than the size of each sheet, so we can consider the sheets infinite. The sheets are uniformly charged, with surface charge densities σ1 and σ2, respectively. The magnitudes and the signs of these charge densities are not known. To determine σ1 and σ2, you measure the electric force on a test point charge q = 2.00 nC at several locations. You find the following results:

i) When the test charge is placed in the region between the sheets, the electric force is 7.92 mN (mili Newtons) and is directed towards sheet 2.

ii) When the test charge is placed in the regions outside, on either side of the sheets, the electric force is 1.12 mN and is directed towards the sheets.

Now address the following questions:

a) Calculate the electric field in the region between the sheets and then in the outside regions. Draw the sheets and sketch some electric field lines in all three regions.
Show neatly your calculations. (15 points)

b) Determine σ1 and σ2. Express your results for σ1 and σ2 in nC/cm2 and do not forget to include the sign. Show neatly your calculations. (20 points)
(Hint: start by expressing the electric fields you just calculated in part a in terms of σ1 and σ2, keeping in mind the principle of superposition. Then solve for the charge densities.)

[Formulas to use: Esheet = 2πk|σ|; F = qE, and the principle of superposition]

A proton moves with a speed of 0.895c.

(a) Calculate its rest energy. _____MeV

(b) Calculate its total energy. ____GeV

(c) Calculate its kinetic energy._____GeV

A radar station locates a sinking ship at range 19.5 km and bearing 136° clockwise from north. From the same station, a rescue plane is at horizontal range 19.6 km, 166° clockwise from north, with elevation 1.95 km.

(a) Write the displacement vector from plane to ship, letting î represent east, ĵ north, and k up.

(b) How far apart are the plane and ship? 2 km

A child hits an ice cube with a mass of 10 grams on a table with a force of 10 N. The impact lasts 0.02 seconds. The ice cube flies off the table, which is 1 meter high and lands some distance away. Assume there is no friction between the ice cube and the table.

a. What is the velocity of the ice cube when it leaves the table?

b. What is the final velocity of the ice cube just before it hits the floor?

c. What is the momentum of the ice cube just before it hits the floor?

d. What distance will the ice cube land from the foot of the table?

e. Suppose the ice cube had broken into two pieces just after the child hit the ice and moved away from each other while falling to the floor. How would the total momentum of the two pieces just before they hit the floor compare to the momentum you found in part (c)?

An inclined plane is sliding, and accelerating, on a horizontal frictionless surface. There is a block at rest on the sloping surface, held in place by a static friction through the horizontal acceleration of the system. the coefficient of static friction between the block and the inclined plane is 0.615. the slope of the incline plane is 42.5 degrees with respect to the horizontal.

a) What is the minumum acceleration of the inclined plane for the square block not to slide?

I found a=1.891 m/s^2

b) what is the maximum acceleration of the inclined plane for the square block not to slide?

To apply the concept of base of support, have a partner stand with his or her feet together and see how much force you must apply to move him or her off balance. Then, have your partner stand with the feet farther apart and repeat your attempts to push him or her off balance. Explain the concept behind how the two differ and how a patient would use this concept if he had balance difficulties and did not use assistive devices to walk

In your own words explain why the force and acceleration vectors in Uniform Circular Motion point inward. Also discuss the differences between Centripetal Force and Centrifugal Force.

Two masses, m1 and m2, are falling but not freely. In addition to gravity, there is also a force F1 applied directly to m1 in the downward direction and a force F2 applied directly to m2 in the horizontal direction. Friction (µs) is present between the two masses and the forces are applied such that they do not rotate. The force F2 is as large as it can be and not have m2 slide relative to m1. (a) Find an expression for the acceleration of the center of mass of the m1 + m2 system in terms of m1, m2, F1, F2, and g? (b) Draw a FBD for each mass separately. Identify motion constraints and Newton's 3rd law force pairs. (c) Write down Newton's 2nd law applied to each mass separately. (d) If both masses are each 2 kg, the coefficient of static friction between the surface is µs = 1/2, and F1 = 25 N, What is the value of F2?

The optimal x-ray energy for producing high contrast images is approximately in the range 20-40 keV. In terms of what we know about how x-rays interact with atoms, discuss the main mechanisms that determine this optimal range and what happens to the images for energies outside this range.?

In one measurement the following values were obtained :

mass of the substance: M=1.3kg,

Power used : P=8.1W

Slope of the Temp vs Time: S=0.027 ^oC/sec.

Knowing that the error on each measured value was 5%

the error on specific heat capacity is (in J/(kg ^oC)

(values may be non-physical )