HW10 Solutions (due Tues, Apr 7)

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1 HW10 Solutions (due Tues, Apr 7) 1. T&M 40.P.066 The total energy consumed in the United States in 1 y is approximately about 7.0 x J. How many kilograms of 235 U would be needed to provide this amount of energy if we assume that 200 MeV of energy is released by each fissioning uranium nucleus, that all of the uranium atoms undergo fission, and that all of the energy-conversion mechanisms used are 100% efficient? 2. T&M 40.P.050 The fusion reaction between 2 H and 3 H is shown below.

2 3 H + 2 H 4 He + n MeV Using the conservation of momentum and the given Q value, find the final energies of both the 4 He nucleus and the neutron, assuming the initial kinetic energy of the system is 1.00 MeV and the initial momentum of the system is zero. Energy conservation: m 3 H c 2 + m 2 H c 2 + K i = m 4 He c 2 + m n c 2 + K n + K He " (m 3 H + m 2 H # m 4 He # m n )c 2 + K i = Q + K i = K n + K He

3 3. T&M 25.P.034 An accelerator produces a beam of protons with a circular cross section that is 2.0 mm in diameter and has a current of 1.0 ma. The current density is uniformly distributed throughout the beam. The kinetic energy of each proton is 20 MeV. The beam strikes a metal target and is absorbed by the target. (a) What is the number density of the protons in the beam? (b) How many protons strike the target in each minute? (c) What is the magnitude of the current density in this beam?

5 4. T&M 25.P.036 The solar wind consists of protons from the Sun moving toward Earth (the wind actually consists of about 95% protons). The number density of protons at a distance from the Sun equal to the orbital radius of Earth is about 7.0 protons per cubic centimeter. Your research team monitors a satellite that is in orbit around the sun at a distance from the Sun equal to Earth's orbital radius. You are in charge of the satellite's mass spectrometer, an instrument used to measure the composition and intensity of the solar wind. The aperture of your spectrometer is a circle of radius 25 cm. The rate of collection of protons by the spectrometer is such that they constitute a measured current of 85 na. What is the speed of the protons in the solar wind? (Assume the protons enter the aperture at normal incidence.) 5. T&M 25.P.037 A gold wire has a 0.10 mm diameter cross section. Opposite ends of this wire are connected to the terminals of a 1.5 V battery. If the length of the wire is 7.5 cm, how much time, on

6 average, is required for electrons leaving the negative terminal of the battery to reach the positive terminal? Assume the resistivity of gold is Ω m.

7 6. T&M 25.P.046 Currents up to 30 A can be carried by 10 gauge copper wire. (a) What is the resistance of 100 m of 10 gauge copper wire? (b) What is the electric field in the wire when the current is 30 A? (c) How long does it take for an electron to travel 100 m in the wire when the current is 30 A?

8 7. T&M 25.P.053 At what temperature will the resistance of a copper wire be

9 10% greater than it is at 20 C? 8. T&M 36.P.061 A battery has an emf of 12.0 V. How much work does it do in 5.0 s if it delivers a current of 3.0 A?

10 9. T&M 25.P.073 A 5.00 V power supply has an internal resistance of 50.0 Ω. What is the smallest resistor that can be put in series with the power supply so that the voltage drop across the resistor is larger than 4.50 V? 9. T&M 25.P.075 Consider the resistor network shown in the figure below, where R 1 = 1 and R 2 = 8. (a) Find the equivalent resistance between points a and b in

11 the Figure. (b) If the potential drop between a and b is 12 V, find the current in each resistor. 11. T&M 25.P.085

12 In the circuit in the figure below, the batteries have negligible internal resistance. (a) Find the magnitude of the current in each resistor. (b) Find the magnitude of the potential difference between points a and b. (c) Find the power supplied by each battery.

13 12. T&M 25.P.095 For the circuit shown in the figure below, C = 6.00 µf, = 100 V, and R = 500 Ω. After having been at contact a for a long time, the switch throw is rotated to contact b. (a) What is the charge on the upper plate of the capacitor just as the switch throw is moved to contact b? (b) What is the current just after the switch throw is rotated to contact b? (c) What is the time constant of this circuit? (d) How much charge is on the upper plate of the capacitor 6.00 ms after the switch throw is rotated to contact b?

14 13. T&M 25.P.082 The batteries in the circuit in the figure below have negligible internal resistance. (Use the following variables as necessary: V = 12 V and R = 6 Ω.) (a) Find the current using Kirchhoff's loop rule. (b) Find the power delivered to or supplied by each battery. (c) Find the rate of Joule heating in each resistor.

15 14. T&M 25.P.032 A thin nonconducting ring that has a radius a and a linear charge density λ rotates with angular speed ω about an axis through its center and perpendicular to the plane of the ring. Find the current of the ring. (Use a for a, lambda for λ, and omega for ω as necessary.)

16 15. T&M 25.P.089 For the circuit in the figure below, V = 1 V and R = 4. Find the potential difference between points a and b.

17 15. T&M 25.P.097 In the circuit in the figure below, the emf equals 50 V and the capacitance equals 2.00 µf. Switch S is opened after having been closed for a long time, and 4.00 s later the voltage drop across the resistor is 20 V. Find the resistance of the resistor.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) If the voltage at a point in space is zero, then the electric field must be A) zero. B) positive.