A particle of mass 'm' moves along straight line and is attracted towards a point on this line with a force proportional to the distance 'x' from that point. The Lagrangian of the system is mv² + kx² O mu² - kx? mv? + kx?
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- A 200.0 kg rocket is launched directly upward from Earth at 9.00 km/s (rE = 6.38 x 10^6 m,mE = 5.98 x 10^24 kg, G = 6.67 x 10^-11)a) What altitude above Earth’s surface does the rocket reach? b) What is the binding energy at that altitude?A particle of rest mass m0 is moving with a speed of 1/2 √3 c. Determine the kinetic energy of the particle in units of E0 !The IKAROS spacecraft, launched in 2010, was designed to test the feasibility of solar sails for spacecraft propulsion. These large, ultralight sails are pushed on by the force of light from the sun, so the spacecraft doesn't need to carry any fuel. The force on IKAROS's sails was measured to be 1.12 mNmN. If this were the only force acting on the 290 kg spacecraft, by how much would its speed increase after 7.0 months of flight? Assume there are 30 days in each month.
- What are (a) the kinetic energy, (b) the rest energy, and (c) the total energy of a 1.2 g particle with a speed of 0.80 c ? Part A Express your answer using two significant figures. ΜΕ ΑΣΦ Ekinetic=263 Submit Previous Answers Request Answer × Incorrect; Try Again; 5 attempts remaining Part B Express your answer using two significant figures. ΜΕ ΑΣΦ Erest = Submit Request Answer Part C Express your answer using two significant figures. ΜΕ ΑΣΦ Etotal = Submit Request Answer ? ? ? J J JIn special relativity, we introduced the momentum of a particle in a given Lorentz frame as pu = (E, pi ), where E is the energy of the particle and pi is the relativistic 3-momentum. Explain why, in general relativity, the energy of a particle measured by an observer is given, irrespective of the coordinate system used, by −p · uobs, where pu is the momentum of the particle and uuobs is the velocity of the observer in those coordinates.The kinetic energy of a mass moving in the x-y plane is: T = mx² + my² Using the transformation = rcos (0) and y = rsin (0), derive a general expression for kinetic energy of the mass in the r, basis.
- [Special Relativity] Two hypothetical X particles, each with mass m, collide head-on with the same magnitude of momentum, in the lab frame. The collision produces two new Y particles, each with mass 2m. What is the minimum kinetic energy, in the lab frame, of each X particle to achieve this process? O a. √2m O b. √3m O c. m O d. 2m.Given: R(N)=f(N)g(N) where f(N) = 7.2N and g(N) = (1 - 7.9/N. If R(N) = H means that R'(N) = 0 and H = 10.5N, what is the value of N that causes R'(N) = 0?A particle has γ=18,399. a)Calculate c-v in m/s. (I would have asked for 1 - v/c, making the answer dimensionless, but the system doesn't seem to take numbers that small. Gamma is chosen to make the particle extremely close to the speed of light.) If your calculator gives problems, you might want to solve the appropriate equation for c-v or c(1 - v/c) and use an approximation. b) In the previous problem, in a race to the moon, by 3/4ths the distance, light is one or ten meters ahead of the particle. We routinely approximate mass as zero, gamma as infinite, and speed as the speed of light. ("Massless particles" -- gamma and m have to be eliminated from the expressions. Light is a true massless particle.) If a massless particle has momentum 1,739 MeV/c, calculate its energy in MeV.
- Uranium-238 decays via the alpha decay process. Part (a) Calculate the energy released in units of megaelectron volts when a uranium-238 nucleus undergoes alpha decay. Part (b) What fraction of the mass of a single uranium-238 nucleus is destroyed in the decay? Part (c) Why is difficult to observe the change in mass for a macroscopic sample of uranium-238?An experimentalist in a laboratory finds that a particle has a helical path. The position of this particle in the laboratory frme is given by r(t)= R cos(wt)i + R sin(wt)j + vztk R,vz, and w are constants. A moving frame has velocity (Vm)L= vzk relative to the laboratory frame. In vector form: A)What is the path of the partical in the moving frame? B)what is the velocity of the particle as a function of time relative to the moving frame? C)What is the acceleration of the particle in each frame? D)How should the accelerartion in each frame be realted?Does your answer to part c make sense?dx 4x 3. In so-called "natural units" (which is just a sneaky way to let us ignore a bunch of constants), the relativistic kinetic energy of a rigid body is given by the formula 1 КЕ — т V1 – v2 where m is the rest mass of the body and v is its relative speed. Alien scientists on a space station are observing an object falling into a black hole. As the object falls, it is disintegrating, losing mass at a rate of 3 (so its mass is changing at a rate of -3). How fast is the kinetic energy of the main part of the object changing when its mass is 20, its velocity is .7, and it is accelerating at a rate of .1 (remember that acceleration is the derivative of velocity with respect to time: a = dt 1Note that this formula does not make sense when v > 1. That is because in natural units, a speed of 1 corresponds to the speed of light, and nothing with positive rest mass can go that fast.