39.39. A proton moves at 0.950c. Calculate its (a) rest energy, (b) total energy, and (c) kinetic energy.
39.40. A cube of steel has a volume of 1.00 cm3 and a mass of 8.00 g when at rest on the Earth. If this cube is now given a speed of u = 0.900c, what is its density as measured by a stationary observer? Note that relativistic density is ER/c2V.
39.43. Show that the energy-momentum relationship E2 = p2c2 + (mc2)2 follows from the expressions E = mc2 and p = mu.
39.44. In a typical color television picture tube, the electrons are accelerated through a potential difference of 25,000 V. (a) What speed do the electrons have when they strike the screen? (b) What is their kinetic energy in joules?
39.47. A pion at rest (m = 270me) decays to a muon (m = 206me) and an antineutrino (mv 0). The reaction is written -- + ˉv. Find the kinetic energy of the muon and the antineutrino in electron volts. (Hint: Conserve both energy and momentum.)
39.51. In a nuclear power plant the fuel rods last 3 yr. before they are replaced. If a plant with rated thermal power 1.00 GW operated at 80.0% efficiency capacity for the 3 yr., what is the loss of mass of the fuel?
39.53. The power output of the Sun is 3.77 x 1026 W. How much mass is converted to energy in the Sun each second?
39.54. A gamma ray (a high-energy photon of light) can produce an electron (e-) and a positron (e+) when it enters the electric field of a heavy nucleus: e+ + e-. What minimum -ray energy is required to accomplish this task? (Note: The mass of the electron and the positron are equal.)
39.61. The net nuclear fusion reaction inside the Sun can be written as
41H → 4He + ΔE. The rest energy of each hydrogen atom is 938.78 MeV and the rest energy of the helium-4 atom is 728.4 MeV. Calculate the percentage of the starting mass that is transformed to other forms of energy.
39.69.A particle with electric charge qmoves along a straight line in a uniform electric field E with a speed of u. The electric force exerted on the charge is qE. The motion and the electric field are both in the x-direction.(a)Show that the acceleration of the particle in the x-direction is given by:
(b) Discuss the significance of the dependence of the acceleration on the speed. (c)What if?If the particle starts from rest at x = 0 at t = 0, how would you proceed to find the speed of the particle and its position at time t?
39.In_Class. Starting from first principles, derive Einstein’s mass-energy equivalence equation E = mc2.
40.3. A black body at 7500 K consists of an opening of diameter 0.0500 mm, looking into an oven. Find the number of photons per second escaping the hole and having wavelengths between 500 nm and 501 nm.
40.5. The radius of our Sun is 6.96 x 108 m, and its total power output is 3.77 x 1026 W. (a) Assuming that the Sun’s surface emits as a black body, calculate its surface temperature. (b) Using the result of part (a), find max for the Sun.
40.9. An FM radio transmitter has a power output of 150 kW and operates at a frequency of 99.7 MHz. How many photons per second does the transmitter emit?