A single point charge +Q is at the center of a thin spherical sheet that carries a net charge of – 3Q and has a radius of a. Your goal is to calculate the electric field at a distance r away from the center of the spherical sheet.
(A) Draw the situation below. Represent a in your diagram. You should NOT have r in your diagram.










(B) Use Gauss’s law to calculate the electric field when r < a (i.e., inside the spherical sheet). a. What surface should you use in order to do this? Draw this surface on your diagram above. b. Use Gauss’s law to calculate the electric field inside the spherical shell.









(C) Use Gauss’s law to calculate the electric field when r > a (i.e., outside the spherical shell) a. What surface should you use in order to do this. Draw this surface on the diagram above. b. Use Gauss’s law to calculate the electric field outside the spherical shell.








(D) On the coordinate axes below, plot the electric field magnitude as a function of r. Hint: The electric field is a piece-wise defined function with different expressions in different regions

A 3.3 kg object is pulled by 4 ropes. One rope is used to pull the object 15° North of East with a force of 25 N. A second rope pulls it due south with a force of 15 N. A third pulls the object 22° west of north with a 36 N magnitude. If the object is moving due west with a constant acceleration (a=1.0 m/s^2 ), describe the force (magnitude and direction) applied by the 4th rope.

A group of particles is traveling in a magnetic field of unknown magnitude and direction. You observe that a proton moving at 1.70 km/skm/s in the +x+x-direction experiences a force of 2.06×10⁻¹⁶ NN in the +y+y-direction, and an electron moving at 4.70 km/skm/s in the −z−z-direction experiences a force of 8.10×10⁻¹⁶ NN in the +y+y-direction.

What is the magnitude of the magnetic field?

What is the direction of the magnetic field? (in the xzxz-plane)

What is the magnitude of the magnetic force on an electron moving in the −y−y-direction at 3.60 km/skm/s ?

What is the direction of this the magnetic force? (in the xzxz-plane)

A magnifying glass uses a converging lens with a focal length of 15.5 cm. It produces a virtual and upright image that is 2.9 times larger than the object.

A) How far is the object from the lens?

B) What is the image distance?

A car traveling 37.0 m/s overtakes another car going only 21.0 m/s. When the faster car is still behind the slower one, it sounds a horn of frequency 1400.0Hz. What is the frequency heard by the driver of the slower car?

You have a rocket with a mass of 2.5kg, that provides a total forward force of F=49N. a.) At what angle must you launch it so that it flies perfectly horizontally. b.) Now you set it up to launch vertically. From rest it takes off but it only has enough fuel to burn for 10 seconds. How high does it get? c.) If it launched at 45 degrees, the fuel burnt for 10 seconds, then it fell to the ground, how far away from its original position would it land?

5. Give an example of a real-world system that looks nothing like a mass on a spring but still behaves like a harmonic oscillator. The weirder the better!

can you please explain the example as well

A converging lens with a focal length of 11.8 cm forms a virtual image 8.35 mm tall, 18.0 cm to the right of the lens.

1.) Determine the position of the object. (answer in cm)

2.) Determine the size of the object. (answer in cm)

3.) Is the image erect or inverted? Select one.

4.) Are the object and image on the same side or opposite sides of the lens? Select one.

The table that follows lists four pairs of initial and final angles of a wheel on a moving car. The elapsed time for each pair of angles is 1.5 s. For each of the four pairs, determine the average angular velocity (magnitude and direction as given by the algebraic sign of your answer).

A 0.294-m-thick sheet of ice covers a lake. The air temperature at the ice surface is -17.7 °C. In 3.00 minutes, the ice thickens by a small amount. Assume that no heat flows from the ground below into the water and that the added ice is very thin compared to 0.294 m. Calculate the number of millimeters by which the ice thickens. Do not enter unit.

1.Calculate the magnitude of the electric field at one corner of a square 1.43 m on a side if the other three corners are occupied by 2.80E-6 C charges

2.Three positive particles of charges Q = 74.1 μC are located at the corners of an equilateral triangle of side L = 15.7 cm, as seen in the figure below. Calculate the magnitude of the net force on each particle.

3.An electron (mass m = 9.11E-31 kg) is accelerated in the uniform field E (E = 1.78E+4 N/C) between two parallel charged plates. The separation of the plates is 1.40 cm. The electron is accelerated from rest near the negative plate and passes through a tiny hole in the positive plate, as seen in the figure below. With what speed does it leave the hole?Show that the gravitational force can be ignored by calculating the ratio of the gravitational to the electric force. Calculate that ratio.

Calculate the final speed of an object if its initial speed is 10 m / s. The object has a mass of 5 kg. Initially it has a height of 20 meters, and it goes down to a height of 15 m. There are no dissipative forces on the object.

An electron is accelerated from rest, at a speed of 0.9995c in a particle accelerator.a) Determine, the resting energy of the electron, b) the total energy (electrons), the kinetic energy in millions of electrons or MeV.

1. This question uses the variables dis (the weighted mean of distances to five Boston employment centers) and nox(nitrogen oxides concentration in parts per 10 million) from the Boston data (library MASS). We will treat dis as the predictor and nox as the response.  

Use the ns() function to fit a natural cubic spline to predict nox using dis. Perform a 5-fold cross-validation in order to select the best degrees of freedom upto 10 degrees.

• Plot degrees of freedom and its cross validation error.
• Plot the resulting fits of the best degrees of freedom.

Please use set.seed(1) on the first line of your R code.

A copper rod is sliding on two conducting rails that make an angle of 20