Match the following: A. Homogeneity of time B. Isotropy of space C. Homogeneity of space D. Bound particle E. Free particle (1) Conservation of total energy (II) Conservation of angular momentum component. (III) Potential energy is not zero. (IV) Conservation of linear momentum. (V) Potential energy is zero. Select the correct choice: (a) A-(IV), B-(II), C (III), D-(I), E-(V) (b) A-(I), B-(II), C (IV), D-(III), E-(V) (c) A-(I), B-(IV), C (II), D-(V), E-(III) (d) A-(IV), B-(II), C (I), D-(III), E-(V)
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- 1. Based on the problem below, if a crew member on the spaceship measures itslength to be 400 m, what is the length measured by an observer on earth? a. 34.2 mb. 44.1 mc. 56.4 md. 78.2 m 2. Based on the problem below, how far does the ship travel in relation to theearth during each pulse? a. 1.35 kmb. 4.21 kmc. 83.8 kmd. 94.5 kmQuestion 5 a). If V=20/x? +y² , find E and D b). State Lorentz force equation c). Find the gradient of the following scaler fields i. V = e?sin2xcoshy ii. U = p?zcos2Ø iii. W =10rsin?ecosø1. Using the principles of conservation of energy and momentum, show that in the decay of a pion at rest, to a muon and a neutrino, л->μ+v., the decay products come out back-to-back. What is the total energy of the muon? What is the total energy of the neutrino? At what fraction of the speed of light does the muon move? (Mass of the muon is 105 MeV/c^2. Mass of the pion is 139 MeV/c^2.) lida
- 52. An alternative derivation of the mass-energy formula E, = moc² also given by Einstein, is based on the principle that the location of the center of mass (CM) of an isolated system cannot be changed by any process that occurs inside the system. The Figure below shows a rigid box of length L that rests on a frictionless surface; the mass M of the box is equally divided between its two ends. A burst of electromagnetic radiation of energy E, is emitted by one end of the box. According to classical physics, the radiation has the momentum p = "0%c , and when it is emitted, the box recoils with the speed v z Eo/ so that the total momentum of Mc the system remains zero. After a time t z L/c the radiation reaches the other end of the box and is absorbed there, which brings the box to a stop after having moved the distance S. If the CM of the box is to remain in its original place, the radiation must have transferred mass from one end to the other. Show that this amount of mass is m, = c2.2. Derive an equation to obtain the Ricci tensor from the Einstein tensor.
- 1. One of the objectives of Special Relativity was to make the laws of electricity and magnetism valid for all inertial observers. In particular, Maxwell's wave equation for light's electric field E is given by 3º E/d? – (1/c?)a²E/? = 0 - (a) Show that this equation does not have its mathematical form preserved under Galilean coordinate transformations, í.e., it violates the principle of Galilean relativity. (b) Next, show that this equation is invariant under Lorentz transformations, i.e., it keeps its form and is thus indeed valid for all inertial reference frames in the context of Special Relativity.4. Consider following the following the fusion nuclear reaction: n+p+p→;He. What happens to the different types of potential energies of this system as a result the reaction (i.e. the electrical potential energy and the strong nuclear potential energy)? The atomic mass of He is 3.016029 u. a. The electrical potential energy and the strong nuclear potential energy both increase. b. The electrical potential energy increases and the strong nuclear potential energy decreases. c. The electrical potential energy increases and the strong nuclear potential energy remains the same. d. The electrical potential energy decreases and the strong nuclear potential energy increases. e. The electrical potential energy and the strong nuclear potential energy both decrease.6
- 1. Based on the problem below, the time and length observed by observer onearth compared with that observed by an observer on the spaceship itself hasa difference of a factor of about a. 2b. 5c. 7d. 10 2. Based on the problem below, what is the duration of each light pulse asmeasured by the observer on earth? a. 1.42 EXP-5 sb. 2.54 EXP-6 sc. 2.82 EXP-7 sd. 3.52 EXP-8 s4[Special Relativity] In the lab frame, events A and B have spacetime coordinates of (1 [m], -1 [m]) and (3 [m], 2 [m]), respectively. What is the time separation of events A and B in the lab frame? a. 1[m] b. 4[m] c. 2[m] d. 3[m]