If a particle is in a stationary state, does that mean that the particle is not moving? If a particle moves in empty space with constant momentum p → and hence constant energy E = p2/2m, is it in a stationary state? Explain your answers.
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If a particle is in a stationary state, does that mean that the particle is not moving? If a particle moves in empty space with constant momentum p → and hence constant energy E = p2/2m, is it in a stationary state? Explain your answers.
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- An electron is accelerated inside a parallel plate capacitor. The electron leaves the negative plate with à negligible initial velocity and then after the acceleration it hits the positive plate with a final velocity B. The distance between the plates is 11.6 cm, and the voltage difference is 107 kV. Determine the final velocity B of the electron using classical mechanics. (The rest mass of the electron is 9.11x1031 kg, the rest energy of the electron is 511 kev.) 6.471x10-1 You are correct. Your receipt no. is 151-494 e Previous Tries What is the final velocity B of the electron if you use relativistic mechanics? 0.948*10°8 Submit Answer Incorrect. Tries 8/12 Previous Tries Send Feedback Post DiscussionConsider a model of an electron as a hollow sphere with radius R and the electron charge -e spread uniformly over that surface. d. Use Einstein’s equation relating rest mass to energy to derive a value for R. Unfortunately, your answer will be model-dependent. The traditional “Classical radius of the electron” is derived by setting the electrostatic work to be e2/(4pi e0 R)Problem 2 The relativistic Lagrangian for a particle of rest mass m moving along the x-axis in a potential V(x) is given by 2 L = -mc² 1 V(x) c2 (a) Derive the Euler-Lagrange equation of motion. (b) Show that it reduces to Newton's equation in the limit |*| << c. (c) Compute the Hamiltonian H of the system. Eliminate ȧ from the Hamiltonian by using the equation ƏL p = ax and write H = H(p, x) as a function of x and p only.
- Calculate the classical momentum of an electron traveling at 0.994c, neglecting relativistic effects. (Use 9.11 ✕ 10−31 for the mass of the electron.)4. The Lagrangian of a relativistic particle is given by v2 L = -moc² 1- where mo is the rest mass of the particle, v is its velocity, and V is not velocity dependent. Find the generalized momentum and the Hamiltonian H. It may be shown that the relativistic kinetic energy T is -moc² (1-2) - V. Check that H = T + V.Determine the linear momentum of an electron moving with 0.10c State your answer in multiples of mec the nearest 0.001mec
- A.8. Show with the aid of the Lorentz transformation (A.28) that the quantity c²₁² — x² - y² – z² is an invariant, namely c²1² − (.x² + ¸‚µ‚² + =²) = (²² 1¹² — (x²² + 1,²² 1₁² +=²²)Suppose an alpha particle (which has a mass of 6.645 × 10-27 kg) is moving at 0.29c.Randomized Variablesv = 0.29 c Part A) What is the momentum of the alpha particle in kg ⋅ m/s?Your video analysis of the motion of a marble gives it position in frame 23 as (x23, 923) = (0.134 m, 0.120 m) and its position in frame 24 as (x24, Y24) = (0.122 m, 0.112 m). You esti- mate that you can measure the x and y positions with uncertainty +0.003 m. The frame rate of the video is 30 frames/s, which means the time interval between frames is At = 0.033 333 s. The uncertainty of the frame rate of a video camera is VERY small. For the sake of this prob- lem, use (At) = 1 x 10-6 s. The mass of the marble is (2.031 +0.001) x 10-2 kg. Calculate the following quantities: 1. The value of the velocity component U = Xi+1Xi At and its uncertainty, Yi+1 Yi = and its uncertainty, At 2. The value of the velocity component vy 3. The value of the velocity magnitude v = 4. The value of the momentum component p 5. The value of the momentum component Py = muy and its uncertainty, and 6. The value of the kinetic energy K = =mv² = m(v²+v²) and its uncertainty. v2+2 and its uncertainty, = mv, and…
- Show that the energy–momentum relationship as shown, E2 = p2c2 +(mc2)2, follows from the expressions E = γmc2 and p = γmu.Two motorcycle pack leaders named Bethany and Keilah are racing at relativistic speeds along perpendicular paths as shown. How fast does Keilah recede as seen by Bethany over her right shoulder?