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placement_phys701_2011 - PHYS 701 Classical Mechanics Fall...

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PHYS 701. Classical Mechanics. Fall 2011 Placement Test This test will not affect your grade in any way. It will be used to evaluate your prior knowledge. Solve as many problems as you can. You are not expected to solve all of them (though it would be nice). 1 Projectiles A cannonball of mass m is shot with a velocity v . At some point on its trajectory it explodes and creates two pieces of mass m/ 2 each. One of the pieces flies horizontally with velocity v/ 2, and the other flies downward with a velocity v/ 2. Find the height at which the explosion took place. v v/2 v/2 2 Collisions-1 A cannonball of radius R and mass M flies with the velocity v . It encounters a hive of bees and goes through it. The thickness of the hive is d . The concen- tration of the bees is n (bees/m 3 ) and the mass of each bee is m ¿ M . When the ball hits the bee it is killed and sticks to the ball. How many bees will be killed? What is the velocity of the ball after the encounter? v d R 3 Collisions-2 A ball moving with velocity v hits a wall moving with velocity u < v . The collision is elastic. What is the velocity of the ball after reflection?
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