Prove that if momentum of a system of particles is constant or conserved then the centre of mass is either at rest or in uniform motion with constant velocity.
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Prove that if momentum of a system of particles is constant or conserved then the centre of mass is either at rest or in uniform motion with constant velocity.
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- H)if m, = Skg, m, = 25kg,u, = 4.5m/s and 8 = 30°, find the final speeds v and vy of the two objects. %3D i) Prove if the collision is elastic or inelastic? m2 m2Three particles of masses m1 = 2.5 kg, m2 = 4.1 kg and m3 = 3.1kg are atthe corners of an equilateral triangle of side 100 cm. If the particle m1 is located at theorigin Find the center of mass of the whole system. and Write the position of the center in unit-vector notation.Use rectangles to create a region such that the center of mass lies outside of the region. Verify algebraically that the center of mass lies outside of the region,
- A stone is dropped at t = 0. A second stone, with 3 times the mass of the first, is dropped from the same point at t=130 ms. (a) How far below the release point is the center of mass of the two stones at t = 260 ms? (Neither stone has yet reached the ground.) (b) How fast is the center of mass of the two-stone system moving at that time? (a) Number (b) Number eTextbook and Media Units Unitsplease i need the full answer with the stepsThe sphere of mass m1 = 5 kg falls from a height H = 1.4 m onto the homogeneous board of negligible mass. The board can rotate around a horizontal axis passing through point O, and a body of mass m2 = 3.9 kg is placed on it at a distance b = 1 m from the axis of rotation. The collision is perfectly inelastic. How high does the body of mass m2 rise after the collision (in m) if a = 0.5 m?
- A billiard ball moving at 5.95 m/s strikes a stationary ball of the same mass. After the collision, the first ball moves at 4.93 m/s, at an angle of 34° with respect to the original line of motion. (a) Find the velocity (magnitude and direction) of the second ball after collision. (Enter the direction with respect to the original line of motion. Include the sign of your answer. Consider the sign of the first ball's angle.) m/s (b) was the collision inelastic or elastic? O inelastic O elasticFind the center of mass of a rod of length L whose mass density changes from one end to the other quadratically. That is, if the rod is laid out along the x-axis with one end at the origin and the of end at x = L, the density is given by p(x) = Po + (P, - PoE where Po and e, are constant values. (Use the following as necessary: L, Po, and e,.) XCM =A uniform rod of length 0.8 m and mass 2.2 kg, has two point masses at each end. The point mass on the left end has a mass 1.5 kg, and the one on the right end has a mass 2.5 kg. Calculate the location of the center of mass of this system in terms of the distance from the left end.