# Physics 101 â Challenge Problems Spring 2015

Physics 101 â Challenge ProblemsSpring 2015Due Tuesday, April 21CHAPTER 9 â Linear Momentum1. A 2 block slides along a frictionless tabletopat 8.0 / toward a second block (at rest) ofmass 4.0 . A massless spring with springconstant = 850 / is attached to the secondblock (see picture). (a) What will be themaximum compression of the spring? (b) What will be the final velocities of the blocks after thecollision? (c) Is the collision elastic?2. A âgravitational slingshotâ is where a spacecraft undergoesan elastic collision with a planet without touching it, inorder to increase its speed and change its direction withoutusing any fuel. The picture to the right shows the planetSaturn moving in the negative x direction at its orbitalspeed (with respect to the Sun) of = −9.5 /. Themass of Saturn is 5.69 Ã 1026 . A spacecraft with amass of 820 approaches Saturn. When far from Saturnit moves in the +x direction at = 10.3 /. The gravitational attraction of Saturn (a conservativeforce) acting on the spacecraft causes it to swing around the planet and head off in the oppositedirection. Estimate the final speed of the spacecraft â after it is far enough away to be considered freeof Saturnâs gravitational pull.3. We derived the rocket equation in class for a rocket in empty space with no gravity. Re-derive theequation for a rocket launching from Earth, with the force of gravity (assume itâs constant, i.e., therocket never gets very far from the Earthâs surface) acting on it. What is the final velocity of the rocketafter it has burned all its fuel? Given the results, why do rocket launches looks so spectacular?1

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