Classical Mechanics

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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