The kinetic energy of a mass m moving from x = 0 to z = d is given by K(x) = Ko (2 – 2). Find the force acting on the mass, and the time that the mass moves from x = 0 to x = d.
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A: Hey dear I have uploaded the images in step 2 and 3 . Have a look
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- Prove the following equation Pw(x,t)= py(x,t) with p=2 ww in (2x-1) Knowing that y (x,t)= 3e^Derive the Lorentz transformation connecting a frame S (the lab frame) to a frame S′ that moves with respect to S with a velocity in the xy plane. This velocity makes an angle ϕ with the x axis of SS and has speed v. In order to solve this, take the route of two successive Lorentz transformations, one along the x axis followed by one along the y axis.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.
- An asteroid of mass 1000 kg travels through space with speed a) What is the total energy of the asteroid? (You can leave your response as a math function, but please simplify as much as you can.) b) The asteroid has a rest length of 20 m. What length would an observer on Earth see? (You can leave your response as a math function, but please simplify as much as you can.)How much energy is required to move a satellite of mass 1000 kg from the surface of the Earth to an altitude 3 times the radius of the Earth? Compute the energy in joules.Consider two particles: p at the origin (0,0,0) = R³ with mass M > 0, and q at the point/position vector 7 = (x, y, z) = R³ with mass m > 0. Let G be the universal gravitational constant. (We will assume the MKS system of units.) The force F = F (7) felt by the particle q due to its gravitational interaction with particle p is: GMm 7(7)= == 7, for all 7 = (x, y, z) € R³\{0} . 17 Also consider the function ƒ : R³\{♂} → R given by GMm f(x, y, z) := TT , for all 7 = (x, y, z) € R³\{0} . Fix an arbitrary point/position vector = (x, y, z) in R³\{♂}. 2, calculate the (3) Calculat cade of the vector (4) Calculate the direction of the vector ₹(7). (5) Assume that is the total force on the particle q. Calculate the instantaneous acceleration, d, of the particle q when it is at the point 7 = (x, y, z).