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Prove that in a one-dimensional elastic collision of two equal masses, the particles simply exchange velocities during collisions.
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- In an elastic collision of two particles with masses m1 and m2, the initial velocities are u1 and u2 = u1. If the initial kinetic energies of the two particles are equal, find the conditions on u1/u2 and m1/m2 such that m1 is at rest after the collision. Examine both cases for the sign of .An object A moving with velocity v collides with a stationary object B. After the collision, A is moving with velocity 2 1 v and B with velocity 3 2 v. Find the ratio of their masses. If, instead of bouncing apart, the two bodies stuck together after the collision, with what velocity would they then move?How does mass appear to affect the final velocities of both elastic and inelastic collisions?
- Direct central impact occurs between a 20lb body moving with a velocity of 3fps and a 30 lb body moving in the opposite direction with a velocity of 6 fps. The 20lb body rebounds in the opposite direction with a velocity of 5fps. Compute the amount and direction of the velocity of the 30 lb body.A ball of mass, m, = 100g, traveling with a velocity V = 50 cm/sec collides “head-on" with a ball of mass m, = 200g which is, initially at rest. Calculate the final velocities, V, and V2p in the event that the collision is elastic.A neutron with mass m1 moving with velocity v0 collides elastically and head-on with a target particle with mass m2 that is at rest. After the collision, the neutron moves with velocity v1f and the target particle moves with velocity v2f. Write the two equations that express conservation of momentum and conservation of kinetic energy for this collision. Consider collisions of the neutron (mass = 1.0 atomic mass unit (amu)) with the following stationary target particles an electron (mass =5 x 10-4 amu) a proton (mass = 1.0 amu) the nucleus of a carbon atom (mass = 12.0 amu) the nucleus of a uranium atom (mass = 238 amu) Match some of the collisions above with each of the following head-on collisions that we discussed in lecture: the collision between two billiard balls, one of the billiard balls initially at rest the collision between a ping pong ball and a bowling ball, the ping pong ball initially at rest the collision between a ping pong ball and a bowling ball, the bowling…
- Show solution A particle A, of mass 8 kg, collides with a particle B, of mass m2 kg. The velocity of particle A before the collision was 5 m/s and the velocity of particle B before the collision was 2.2 m/s. Given the velocity of particle A after the collision was -4 m/s, and the velocity of particle B was 3 m/s, what was the mass of particle B?In this problem, the distance units are meters and the time units are sec- onds. Consider two particles p and q in 2-D or 3-D space, with respective masses n kg and m kg, that approach cach other, collide elastically, and then bounce off. Suppose is the initial constant velocity of p, and is the initial velocity of q (see the "Before Collision" picture below). After the collision, p and q have constant velocities of uƒ ‡ ♂ and vƒ ‡ ♂, respectively (see the "After Collision" picture below). Beforedli the stepeni ullision After the collision collision point 2-D р Constant 3-D 2 • V 6 Constant) velocities (1) Calculate a formula for the radian angle 0 € [0, π] between the path of p and the path of q after the collision, in terms of the scalar quantities m, n, |||| and |||| (and only these quantities). (2) In the case where p and q have the same mass, calculate exactly.A cube measuring bxbxb with mass m was initially resting on a flat horzontal surface. The minimum inpulse needed to cause tipping was found to be: Lmin= m[(2gb/3)(21/2-1)]1/2 If the impulse is increased to 2Lmin find the kinetic energy of the cube when side OA hits the ground.
- A ball of mass 8 kg and moving to the right has a velocity of 8.2 m/s and is in a head-on collision with another ball of mass 4.8 kg and moving to the left at 4.6 m/s. Determine their final velocities if the collision is perfectly elastic and perfectly inelastic. Illustrate the motion.A proton that has a mass m and is moving @ 400m/s in the +i direction undergoes a head-on elastic collision with a stationary oxygen nucleus of mass 16m. Find the velocities of the proton and the oxygen nucleaus after the collision.Two particles of equal mass collide. Before the collision, particle A has initial velocity VA, while particle B is at rest. After the collision, the angle of deflection of particle A is 0,=30°. Assume, at first (in parts a and b), that the collision if elastic. (a) Find the angle of deflection of particle B. (b) Assume that the velocity of particle A before the collision is VA = 100 m/s and that the kinetic energy of particle B after the collision is Kg' = 20 J. Find the particles' mass. (c) If, instead, the collision is fully inelastic, what is the angle of deflection and the velocity of the combined A+B particle after the collision?