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An observer moving at a speed of 0.995c relative to a rod (see figure below) measures its length to be 2.50 m and sees its length to be oriented at...

1. An observer moving at a speed of 0.995c relative to a rod (see figure below) measures its length to be 2.50 m and sees its length to be oriented at 29.00° with respect to the direction of motion.
(a) What is the proper length of the rod?
(b) What is the orientation angle in a reference frame moving with the rod?

2. In a Young's interference experiment, the two slits are separated by 0.17 mm and the incident light includes two wavelengths: λ1 = 540 nm (green) and λ2 = 450 nm (blue). The overlapping interference patterns are observed on a screen 1.38 m from the slits.
(a) Find a relationship between the orders m1 and m2 that determines where a bright fringe of the green light coincides with a bright fringe of the blue light. (The order m1 is associated with λ1, and m2 is associated with λ2.)
m2/m1 =

(b) Find the minimum values of m1 and m2 such that the overlapping of the bright fringes will occur and find the position of the overlap on the screen.
m1 =

m2 =

Distance =

3. The work function for silver is 4.26 eV.
(a) Convert the value of the work function from electron volts to joules.
1 J

(b) Find the cutoff frequency for silver.
2 Hz

(c) What maximum wavelength of light incident on silver releases photoelectrons from the silver's surface?
3 m

(d) If light of energy 8.6 eV is incident on silver, what is the maximum kinetic energy of the ejected photoelectrons? Give the answer in electron volts.
4 eV

(e) For photons of energy 8.6 eV, what stopping potential would be required to arrest the current of photoelectrons?
5 V

4. Show (by calculating the velocity in terms of c) that if an electron were confined inside an atomic nucleus of diameter 2.4 10-15 m, it would have to be moving relativistically, whereas a proton confined to the same nucleus can be moving at less than one-tenth the speed of light. (Give all answers to 4 decimal places.)
(a) When the confined particle is an electron, ER = 0.511 MeV.

(b) When the confined particle is a proton, ER = 939 MeV.

6. A hydrogen atom is in its third excited state (n = 4). Using the Bohr theory of the atom, calculate the following.
(a) the radius of the orbit
1 nm

(b) the linear momentum of the electron
2 kg·m/s

(c) the angular momentum of the electron
3 J·s

(d) the kinetic energy
4 eV

(e) the potential energy
5 eV

(f) the total energy
6 eV

7. Three point charges are located at the corners of an equilateral triangle. Find the magnitude and direction of the net electric force on the 1.80 µC charge. (A = 1.80 µC, B = 6.50 µC, and C = -3.80 µC.)
counterclockwise from the +x-axis

8. Two point charges lie along the y-axis. A charge of q1 = -7.5 μC is at y = 6.0 m, and a charge of q2 = -8.5 μC is at y = -4.0 m. Locate the point (other than infinity) at which the total electric field is zero.

9. The resistor R dissipates 16 W of power. Determine the possible values of R. (ΔV = 73 V)

larger value
R =
smaller value
R =

10. Three long, parallel conductors carry currents of I = 3.0 A. The figure below is an end view of the conductors, with each current coming out of the page.

Given that a = 1.6 cm, determine the magnitude and direction of the magnetic field at each of the following points:
(a) point A

(b) point B

(c) point C

11. A series circuit contains a 3.00 H inductor, a 3.80 µF capacitor, and a 25.0 resistor connected to a 120 V (rms) source of variable frequency. Find the power delivered to the circuit when the frequency of the source is each of the following:
(a) the resonance frequency

(b) one-half the resonance frequency

(c) one-fourth the resonance frequency

(d) two times the resonance frequency

(e) four times the resonance frequency

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