Conservation of momentum

         

Two balls roll toward each other on a frictionless floor. The red ball has a mass of 1.00 kg1.00\text{ kg} and a speed of 3.00 m/s.3.00\text{ m/s}. The blue ball has a mass of 5.00 kg5.00\text{ kg} and a speed of 2.00 m/s.2.00 \text{ m/s}. If the balls stick together after the collision, determine the (approximate) final velocity of the balls.

A 200 kg200\text{ kg} bumper car travels at 8 m/s8\text{ m/s} due east. It hits an identical bumper car traveling due north at 8 m/s.8\text{ m/s}. If the two cars lock bumpers and stick together, what is the approximate resulting speed of the cars?

An astronaut floating still in space has a total mass of 201 kg,201\text{ kg}, including his weight and all his equipment. He throws a 1 kg1\text{ kg} wrench with a speed of 10 m/s.10\text{ m/s}. What is the resulting speed of the astronaut?

Ball AA of mass 2 kg2\text{ kg} is rolling on a frictionless horizontal floor at 5 m/s.5\text{ m/s}. It collides head-on with ball BB of mass 3 kg3\text{ kg} which is initially at rest. If we let vAv_A and vBv_B denote the respective velocities of balls AA and BB after the collision, in which of the following situations are the linear momenta conserved?

Define the initial direction that ball AA moves in as positive direction.

Object AA of mass mA=2 kgm_A=2\text{ kg} moves with a velocity of v=2 m/sv=2\text{ m/s} toward a stationary object BB of mass mB=4 kg.m_B=4\text{ kg}. After the impact, objects AA and BB move off in directions that form 3030^\circ and 4545^\circ angles with the initial direction of object A,A, respectively. Assuming that the system is entirely frictionless, what is the speed of object AA after the collision?

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