A rocket is accelerated in flat spacetime due to a constant thrust force F in the x-direction, such that the equation of motion is dp (2) dt where p is the spatial part of the relativistic 4-momentum p.
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Find the energy of this rocket as a function of time
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- There exista a spherical planet with a mass of M and a radius of R. How much energy is required to take a rocket of a mass m from rest on the surface of the planet to a circular orbit a height h above the surface?Find using the Energy Difference Ef -Ei where Ef is the energy in orbit and Ei is the energy at rest on the surface. h is not smallI. With external gravitational field In this second part you are asked to analyze rocket propulsion with the present of gravitational field g. This appears for instance when the rocket is launching from the surface of a planet. (1) Describes why you are not allowed to use the momentum conservation here. (2) Evaluate the speed of the rocket measure by inertial observer on the ground as a function of time v(t) if the speed of the gas propulsion with respect to the rocket is vret and the burning rate is constant constant! dm dt (3) Plot v(t) that you obtained from point (2) above, for three different values of gravitational field (assuming similar initial mass), which is: Imoon = 1.62 m/s? • Gearth = 9.81 m/s? Ijupiter = 24.79 m/s? in a single plot, if the burn dm ate is constant = 1500 kg/s. Analyze your result and dt describes how the speed increases for each situation! 20:18 Ai 11/03/2022We have two spheres (m and M) that are separated by a small distance; m is to the left of M. A sphere of mass m (identical to one of the two initial spheres) is moving towards m at a speed V0. Show that when M is smaller than or equal to m, there will be 2 collisions and calculate the final speeds. Show that when M is larger than m, there will be three collisions and calculate the final velocities.
- Can you please answer this question ASAP A and B have same mass. Initially, B is at rest and A is moving at 5 m/s. If restitution coefficient is 1 , what is the velocity (m/s) for B after impact._____7. The kinetic energy of a mass m moving from x = 0 to x =d is given by K(x) = Ko (2-). Find the force acting on the mass, and the time that the mass moves from x = 0 to x = d.Compute for the mass of an the mystery box. Given: vi=0m/s Vf= 40m/s Time: 19.08 seconds