e) Determine the generalized momenta associated with plane polar coordinates.
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- (a) (i) Write down an expression for the force acting on a charge moving with velocity v in the presence of both electric E and magnetic B fields. Assume that a particle of charge Qmoves in the presence of a uniform magnetic field B. (ii) Find the magnitude of the momentum of the particle if it moves in a circle of radius R in the plane perpendicular to B. Sketch the trajectory of the particle if it has an additional component of velocity v parallel to B. (iii) Show that magnetic forces do no work on a charge Q. (b) Starting from the integral form of Gauss's law, derive the differential form of the law, where p is the charge density. V.E = 1 ·PIn an elastic collision of particles, one particle is stationary and another one is moving to the particle at speed u. After colliding, particle 1 and 2 moves at two different velocity, say v1 and v2. Why is the angle between v1 and v2 must be 90 degrees if the resulting particles and the initial particles all have the same mass?As seen in the image provided, a double-star system with stars of equal mass rotate in circular orbits around their mutual center of mass that is halfway between them. One of the stars (α) is bright. The other star (β) is its unseen dark companion. Our line of sight passes through the orbital plane such that once in every period, α approaches head-on, and once ever period it recedes directly away. The same is true for β. Suppose light always moves at speed c relative to the source that emits it (i.e., if v is the orbital speed of each star, light travels toward us at speed c + v from α when it is headed toward us, and at speed c - v when it is headed away from us, as depicted). The double-star system is a distance d away from Earth. How long would take light to get to Earth from α if the light is emitted when α is (i) coming toward us, and (ii) moving away from us?
- Mechanic Physics: Please make sure this is right In the figure, a ball of mass m = 56 g is shot with speed vi = 23 m/s (in the negative direction of an x axis) into the barrel of a spring gun of mass M = 263 ginitially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. Assume that the increase in thermal energy due to friction between the ball and the barrel is negligible. (a) What is the speed of the spring gun after the ball stops in the barrel? (b)What fraction of the initial kinetic energy of the ball is stored in the spring?I. 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 11/03/2022For 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.
- We 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.Needs Complete typed solution with 100 % accuracy.As seen in the image provided, a double-star system with stars of equal mass rotate in circular orbits around their mutual center of mass that is halfway between them. One of the stars (α) is bright. The other star (β) is its unseen dark companion. Our line of sight passes through the orbital plane such that once in every period, α approaches head-on, and once ever period it recedes directly away. The same is true for β. Suppose light always moves at speed c relative to the source that emits it (i.e., if v is the orbital speed of each star, light travels toward us at speed c + v from α when it is headed toward us, and at speed c - v when it is headed away from us, as depicted). Find a distance d (in terms of v, c, and the orbital period T) such that α would appear to be simultaneously to the left and right of the center of mass point.
- I need the answer as soon as possibleSaved Help Required information of 2 Particle A has a mass of 5.40 g and particle B has a mass of 1.80 g. Particle A is located at the origin and particle B is at the point (x, y) = (25.0 cm, 1.70 cm). What is the x-component of the CM? ook cm Hint rint rences 10 11 of 21 rch...pdf 2 Edje PreLab Arch..pdf