Collected Problems for Test 4

Problem #18 (Due 4/14 Tuesday by 9:00 a.m.)
A Romulan spacecraft has a speed of 0.75c with respect to the planet Vulcan. The Romulans measure 27.0 h for the time interval between two events on Vulcan. What value for the time interval would they measure if their ship had a speed of 0.94c with respect to Vulcan?

Problem #19 (Due 4/17 Friday by 9:00 a.m.)
Suppose you're driving down the highway at a speed of 25 m/s. A truck in the next lane is traveling toward you with a speed of 35 m/s relative to the ground. Relative to you the truck is approaching at a speed of 25 m/s + 35 m/s = 6.0 x 10¹ m/s.
a) Since the speeds are much less than the speed of light, would the relative speed be the same if you were going 5.0 m/s relative to the ground and the truck were moving at 55 m/s relative to the ground? Give a reason for your answer.
b) Suppose the speed of light were c = 65 m/s. Would the relative speeds be the same for the two situations? Give a reason for your answer.
c) Using the data presented above and assuming the speed of light is c = 65 m/s, determine the speed of the truck relative to you for the two situations when your speed and the truck's spare are, respectively, 25 m/s and 35 m/s, and
d) 5.0 m/s and 55 m/s.

Problem #20 (Due 4/21 Tuesday by 9:00 a.m.)
The maximum wavelength for which an electromagnetic wave can eject electrons from a platinum surface is 196 nm. When radiation with a wavelength of 141 nm shines on the surface, what is the maximum speed of the ejected electrons?

Problem #21 (Due 4/24 Friday by 9:00 a.m.)
#21a. Two waste products from nuclear reactors are strontium ⁹⁰₃₈Sr (T_1/2 = 28.5 yr) and cesium ¹³⁴₅₅Cs(T_1/2 = 2.06 yr). These two species are present initially in a ratio of N_0,Sr/N_0,Cs = 7.80 x 10^-3. What is the ratio N_Sr/N_Cs fifteen years later?

#21b. During a nuclear reaction, whether it is a fission reaction or a fusion reaction, energy is released.
a) Is the total mass of the particles after the reaction greater than or less than the total mass of the particles before the reaction?
b) In one type of fusion reaction a proton fuses with a neutron to form a deuterium nucleus: ¹₁H + ¹ ₀n yielding ²₁H. The masses are ¹₁H (1.0078 u), ¹₀n (1.0087 u), and ²₁H (2.0141 u). How much energy (in MeV) is released by this reaction?