Show that if the particles have the same mass, the angle between the scattered particles in the glancing collision is always 90 degrees, regardless of the angle 0. This is useful information for those that shoot pool (
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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 .Prove that in a one-dimensional elastic collision of two equal masses, the particles simply exchange velocities during collisions.How does mass appear to affect the final velocities of both elastic and inelastic collisions?
- Consider a head-on, elastic collision between twobodies whose masses are m and M, with Itis well known that if m has speed and M is initiallyat rest, m will bounce straight back with its speedunchanged, while M will remain at rest (to anexcellent approximation). Use this fact to predict thefinal velocities if M approaches with speed and mis initially at rest.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?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?
- Consider the collision below between two objects of unequal mass. After finding the angle Θ2 speed v2 for the larger mass, show that the collision is elastic.Prove that the linear momentum of a system of particles is conserved.The following figure shows two particles of masses m1 and m2, with velocities before the collision of magnitude v1 and v2. If the collision is perfectly elastic, find the magnitude of the velocities v1' and v2' after the collision and the angle of incidence θ (theta), as a function of the masses and velocities before the collision.
- an object of mass m and velocity v collides elastically with a stationary object and continuies in the same direction with a speed of 0.25v. what is the mass of the object that was initially stationaryAn object initially at rest explodes in two fragments of masses 2.0 kg and 4.6 kg that move indiametrically opposite directions. If the speed of the first fragment is 1.0m/s, find the internalenergy of the explosion.Let it be a system formed by two particles 1 and 2 of mass m1 and m2, respectively. Show that the position of the center of mass is located at an internal point to the line segment that connects the positions of particles 1 and 2. This result allows us to immediately estimate the position of the center of mass of a two-particle system.