Conservation of momentum


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

A \(200\text{ kg}\) bumper car travels at \(8\text{ m/s}\) due east. It hits an identical bumper car traveling due north at \(8\text{ m/s}.\) 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 \(201\text{ kg},\) including his weight and all his equipment. He throws a \(1\text{ kg}\) wrench with a speed of \(10\text{ m/s}.\) What is the resulting speed of the astronaut?

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

Define the initial direction that ball \(A\) moves in as positive direction.

Object \(A\) of mass \(m_A=2\text{ kg}\) moves with a velocity of \(v=2\text{ m/s}\) toward a stationary object \(B\) of mass \(m_B=4\text{ kg}.\) After the impact, objects \(A\) and \(B\) move off in directions that form \(30^\circ\) and \(45^\circ\) angles with the initial direction of object \(A,\) respectively. Assuming that the system is entirely frictionless, what is the speed of object \(A\) after the collision?


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