A linear transformation of a generalised co-ordinates 'q' and the corresponding momentum 'p' to 'Q' and 'P' given by, Q = q + p; P = q + ap Is canonical if the value of the constant a is O-1 2 O 1
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- The observer O notes that the front and back of the rocket simultaneously line up with the ends of the platform at a particular Instant. 0.8c 65 m HITRO (a) -108 m- THƠ 0.8c 0 1-39 ml (b) According to observer O, the ends of the rocket simultaneously line up with the ends of the platform. Are these events simultaneous to O`? Yes Can't be determined May be No .1 .2 3 .4 O Scanned with CamScanneErnest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei (197Au). The energy of the incoming helium nucleus was 7.12 ✕ 10−13 J, and the masses of the helium and gold nuclei were 6.68 ✕ 10−27 kg and 3.29 ✕ 10−25 kg,respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.) (a)If a helium nucleus scatters to an angle of 119° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus. 4He speed ______m/s 197Au velocity____ m/s 197 Au direction 330.36 ° counterclockwise from the +x-axis (b)What is the final kinetic energy (in J) of the helium nucleus? ___________ JShow that the kinetic energy of a particle of mass m is related to the momentum p of that particleby, ? =p^2/2m. (Hint: plug mv in for p and simplify!)
- My last step was F=.57mg/Cos(-15.1)+(0.57 Sin (15.1) Outcome of 0.6977mg I think I found the The condition for moving a block but I don’t know what to do next.I’m confusedErnest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (ªHe) from gold-197 nuclei (197 Au). The energy of the incoming helium nucleus was 7.28 × 10-13 J, and the masses of the helium and gold nuclei were 6.68 × 10-27 kg and 3.29 × 10-25 kg, respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.) (a) If a helium nucleus scatters to an angle of 136° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus. 4He speed 197 Au velocity t 197 Au direction 14500000 0.0140 -17 m/s X m/s ° counterclockwise from the +x-axis (b) What is the final kinetic energy (in J) of the helium nucleus? 7.02e-13 JThe star of a distant solar system explodes as a supernova. At the moment of the explosion, an resting exploration spaceship is 15 AU away from the shock wave. The shock wave of the explosion travels with 25000 km/s toward the spaceship. To save the crew, the spacecraft makes use of a special booster that uniformly accelerates at 150 m/s^2 in the opposite direction. Determine if the crew manages to escape from the shock wave. (Neglect relativistic effects.)
- An electron has a momentum of 2.00 x 10-2¹ kg⋅m/s. Find the kinetic energy of the electron in units of MeV. (A) 2.31 (B) 5.74 (C) 4.97 (D) 3.27 (E) 6.49For an isolated system where two masses collide in two dimensions (2D), check all TRUE statements: Piy = Pfy J = 0, since the x and y components cancel each other out. If the masses collide in 2D, the collision must be inelastic. Pfx =Pix If the collision is inelastic, the final momentum, Pf, can be derived by the vector addition of the momentum vectors of the two masses prior to collision.Helpful information: (1) An alpha particle is a helium nucleus, (2) e = 1.6 × 10-¹⁹ C, (3) k₂ = 9.0 × 10⁹ Nm² C-2, (4) 1nm = 1 × 10-⁹ m 1-An alpha particle lies on the x-axis, a distance of 1.0 nanometer from a proton (in this set-up, the alpha particle is at the origin while the proton is in the positive direction). Which of the following choices below represents the magnitude of the electric force on the alpha particle? (a) 2.3 × 10-10 N (b) 4.6 × 10-10 N (c) 2.3 x 10-19 N (d) 4.6 x 10-19 N cing the voltage so following insta choices below at a time! 1.00 s?
- HELP!The muon is an unstable particle that spontaneously decays into an electron and two neutrinos. In a reference frame in which the muons are stationary, if the number of muons at t = 0 is N0, the number at time t is given by , where τ is the mean lifetime, equal to 2.2 ms. Suppose the muons move at a speed of 0.95 c and there are 5.0 × 104 muons at t = 0. (a) What is the observed lifetime of the muons? (b) How many muons remain after traveling a distance of 3.0 km?To study Brownian motion, Bob, a student at the University of Ottawa, used his camera to capture the positions (i.e. displacements) of 50 microscopic dust particles floating on the surface of the water of his aquarium. By setting his camera to record 10 frames per second and noting down each particle's 2D displacement for each recorded frame, he managed to obtain the following mean-displacement vs time graph: 1600 1400 1200 2 1000 V 800 600 400 200 20 40 60 80 100 120 140 Time (s) a. Use the above mean-displacement graph to roughly approximate the diffusion coefficient D of the dust particles with units of um? /s. b. From the diffusion coefficient estimate in a), calculate the root mean- square displacement expected between each consecutive frame? c. Are the diffusion coefficient D and mean-square displacement calculated reasonable for a microscopic particle, or did Bob make a mistake in his calculations? Mean-square disp. (cm²)