Two low-friction physics demo carts collide on a horizontal track. The first cart, with a mass of 0.154 kg , is moving to the right with a speed of 0.810 m/s . The second cart, with a mass of 0.299 kg , is moving to the left with a speed of 2.21 m/s . The carts collide in an elastic collision, such that the total kinetic energy after the collsion is equal to the total kinetic energy before the collision.

1. What is the final speed of the 0.154 kg cart?

2. What is the direction of the final velocity of the 0.154 kg cart?

3. What is the final speed of the 0.299 kg cart?

4. What is the direction of the final velocity of the 0.299 kg cart?

A.) A scuba diver, submerged under water, looks up and sees sunlight at an angle of 11.0° from the vertical. At what angle, measured from the vertical, does this sunlight strike the surface of the water? Assume water has a refraction index of 1.333.

B.) To focus a camera on objects at different distances, the converging lens is moved toward or away from the image sensor, so a sharp image always falls on the sensor. A camera with a telephoto lens (f = 400 mm) is to be focused on an object located first at a distance of 3.5 m and then at 50.0 m. Over what distance must the lens be movable?

C.) A layer of oil (n = 1.45) floats on an unknown liquid. A ray of light originates in the oil and passes into the unknown liquid. The angle of incidence is 55.0 degrees, and the angle of refraction is 59.1 degrees. What is the index of refraction of the unknown liquid?

D.) A ray of sunlight is passing from diamond into crown glass; the angle of incidence is 25.60°. The indices of refraction for the blue and red components of the ray are: blue (n_diamond = 2.444, n_{crown glass} = 1.531), and red (n_diamond = 2.410, n_{crown glass} = 1.520). Determine the angle between the refracted blue and red rays in the crown glass.

Question 1.

Part A. A proton spit out from the Sun hurtles heads toward Earth -- directly at you! In what direction does the earth's magnetic field nudge it?

North, East, South, or West? Choose One.

Part B: At home during a break from classes, you visit your grandparents who still have a tube-type television, with the deep and heavy case. (In them, a beam of electrons fired from the center rear of the picture tube is steered to 'paint' an image on the front of the tube.)  Their living room is arranged so that the TV is on the north wall of the house, facing south. In which direction, if ever so slightly, does the weak magnetic field of the earth deflect the electron beam inside the tube?

Up, Down, Left, Right or The beam is not affected at all? Choose one.

Part C: Later, you go to the guest room to get ready for bed. Your grandparents have another old tube type television in that room, this time on the west wall, facing east. Now which way are the electrons in the tube deflected, if ever so slightly?

Up, Down, Left, Righ, or Not At All? Choose one.

Part D: A velocity selector, as in the previous question, works to select ions of a particular speed because

-the electric and magnetic fields both depend on the speed of the ions.

-neither the electric nor the magnetic fields depend on the speed of the ions.

-the magnetic force on an ion depends on its speed, but the electric force does not.

-the electric force on an ion depends on its speed, but the magnetic force does not.

Choose one.

An eagle is flying horizontally at 5.7 m/s with a fish in its claws. It accidentally drops the fish.

(a) How much time passes before the fish's speed quadruples?


(b) How much additional time would be required for the fish's speed to quadruple again?

A Spinning Ball: What is the magnetic field inside and outside a uniformly charged solid ball (total charge ?, radius ?) spinning about its axis with angular velocity ? ̂?? Do this three ways:

(a) Set up a Biot-Savart-style integral to determine the field at any location. (Do not solve this integral, but make all quantities explicit.)

(b) Simplify your integral using a location along the axis of rotation: ? = ? ̂? or ? = 0. Solve for ? inside and outside.

(c) Use your result to determine where along the ? axis the magnetic field is the strongest.

A neutron hits U 235 which then splits into a Cs 140 atom (139.91728u), a Rb 93 atom (92.92204u), and several neutrons. How many grams of U 235 do we need to start with to produce 1.3 x 10^9 J?

how does the x-ray circuit influence the production of x rays

Describe the components of Hyper-V and the process for installing it.

2. Critique the following carbon mitigation wedge plan from the perspective of developing nations. Is this friendly to the growth of these nations? Make sure you completely dissect the plan with respect to cost, energy needs, and threat of famine. Your critique should be 100-words or less.

4.22 mode-locked laser (a)consider a He-Ne laser emitting at 632.8nm, and mode-locked. the tube length is 50cm. the spectral with of the optical gain curve is 1.5 GHz Find the mode-locked pulse width and the repetition rate. what is the seperation of pulses in space? (b) consider a Nd^3+ glass laser that is mode-locked. The emission wavelength is 1060 nm and the spectral width of the optical gain curve is 7THz. the refractive index of the laser medium is 1.45. find the mode-locked pulse width and the repetition rate . if the Nd^3+ glass rod is 10cm long, what is the seperation of pules in space?

Mosquitoes are able to find a person’s vein in three stages; at a range of 50 meters the mosquito detects a CO2 plume due to breath, at 10 meters the mosquito is able to see the person in the visible range, and finally inside 20 cm the mosquito can detect the low energy light emitted from our warm veins. If the average body temperature is 37.5 ◦ C and the mosquitoes eye is sensitive enough to detect 10^16 photons per second in the infrared, estimate the surface area of the mosquitoes eye (in mm^2 ). Hint: consider the mosquito at 20 cm from a person’s arm and approximate the arm as a cylinder with a surface area of 4.5% where all radiation leaves perpendicular to the surface the total. You will need: • the average length of a person’s arm ≈ 64 cm. • the average surface area of a person ≈ 1.75 m^2 .

A plane-parallel monoenergetic beam of 1O^I2 uncharged particles per second
is incident perpendicularly on a layer of material 0.02 m thick, having a density
p = 11.3 X lo^3 kg/m3. For values of the mass attenuation coefficient m/p =

1X lo^-3 3 X lo^-4 and 1 X lo^-4 m2/kg, calculate the number of primary par-
ticles transmitted in 1 minute. Compare in each case with the approximation

in Eq. (3.5); give percentage errors.

1) Identical twins Anna and Hannah visit you at the optical clinic. Anna, whose eyes can easily focus on distant objects (her far point), is also able to focus on objects within 20 cm of her eyes (her near point). Assuming the diameter and, hence, the distance between the cornea and retina, of Anna's eye is 20 mm, what is the range (in diopters) of Anna's vision? The limits of this range correspond to the total refractive power of her eyes at their far point and and the refractive power at their near point.

a) from 50 to 50.5 diopters

b) from 50 to 55 diopters

c) from 50 to 60 diopters

d) from 0 to 5 diopters

2) Hannah's eyes have the same range as her sister's, with the same focal power for her cornea (50 diopters) and for her variable lens (5 diopters), but Hannah suffers from myopia. She cannot focus on any object that lies more than 0.7 meters from her eyes since they are slightly longer -- the cornea to retina distance is larger -- than her sister's eyes. Considering this new far point, what is the diameter of Hannah's eyes (in millimeters, to the nearest tenth of a millimeter) assuming Anna's eye diameter was ideally, again, 20.0 mm? Hint: the focal power of the cornea remains the same for Hannah as for Anna for focusing distant objects, but the farthest Hannah can see (object distance) changes from infinity to 0.7 meters.  

3) Assuming, instead, that the diameters of Hannah's myopic eyes were 20.4 mm, but, again, that Hannah's eyes share the same focal powers for her cornea and lens as Anna's, what would be Hannah's near point (to the nearest tenth of a cm, in cm) if Anna's, again, is 20 cm?

4) Now assuming Anna's far point was found to be 0.8 m (i.e., her eyes can't focus on any object more than 0.8 m away), what power corrective lenses would you prescribe to Hannah so that, when wearing these lenses, her visual range was the same as Anna's (from a near point of 20 cm to a far point of infinity? Give your answer in units of diopters, to the nearest tenth of a diopter, with the correct sign.

5) One treatment of cataracts is to surgically remove the variable lens of the eye. If we assume that the cornea's refractive power focuses objects at infinite distances onto the retina of a person who has had this surgery, what power correcting lenses would they need to be able to read text at a 21-cm near-point distance? Again, give your answer in units of diopters, to the nearest tenth of a diopter and with the correct sign.

When violet light and yellow light shine on a metal surface, only one color produces an electric current. Write 3 - 4 sentences describing the effect of each light on the metal. Would increasing the intensity of either type of light have an effect on the current produced? How does quantization help to explain these observations? (6 points) Please don't write too long :)

You have constructed a 5-kg toy iceboat which you set on a frictionless frozen pond when a sudden wind exerts a constant force on the boat of 100 N due west. Due to how you have set the sails, the wind causes the boat to slide 10.0 m in a straight line at 30◦ north of west. What is the speed of the boat at the end of those 10.0 m?