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Unformatted text preview: oldhomewk 26 YOO, HEE Due: Apr 1 2008, 4:00 am 1 Question 1, chap 13, sect 3. part 1 of 2 10 points A wooden block of mass M hangs from a rigid rod of length having negligible mass. The rod is pivoted at its upper end. A bullet of mass m traveling horizontally and normal to the rod with speed v hits the block and gets embedded in it. M v m What is the angular momentum L of the block-bullet system, with respect to the pivot point immediately after the collision? 1. L = M v 2. L = mv correct 3. L = ( m + M ) v 4. L = parenleftbigg M m M + m parenrightbigg v 5. L = ( M- m ) v Explanation: Basic Concepts: If summationdisplay vector ext = 0, then summationdisplay vector L = 0 Solution: The net angular momentum of the system conserves, and we have L i = L f = L, where L = mv . Question 2, chap 13, sect 3. part 2 of 2 10 points What is the fraction K f K i (the final kinetic energy compared to the initial kinetic energy) in the collision? 1. K f K i = m m + M correct 2. K f K i = m M- m 3. K f K i = 2 m m + M 4. K f K i = M M + m 5. K f K i = M M- m Explanation: By conservation of the angular momentum L i = L f = L mv = ( m + M ) v f . Therefore v f = v parenleftbigg m m + M parenrightbigg K i = 1 2 mv 2 K f = 1 2 I 2 f where I = ( M + m ) 2 and f = v f . Thus, K f = 1 2 ( M + m ) v 2 f . The final kinetic energy compared to the ini- tial kinetic energy is K f K i = 1 2 m 2 M + m v 2 1 2 mv 2 = m M + m . Question 3, chap 13, sect 3. part 1 of 2 10 points A small puck of mass 31 g and radius 19 cm slides along an air table with a speed of 1 . 6 m / s. It makes a glazing collision with a oldhomewk 26 YOO, HEE Due: Apr 1 2008, 4:00 am 2 larger puck of radius 50 cm and mass 83 g (ini- tially at rest) such that their rims just touch. The pucks stick together and spin around af- ter the collision. Note: The pucks are disks which have a moments of inertia equal to 1 2 mr 2 . + + 1 . 6 m / s V cm 31 g 83 g (a) (b) (c) 50 cm 19 cm radius Figure: The two pucks: (a) before they collide, (b) at the time of the collision, and (c) after they collide. After the collisions the center-of- mass has a linear velocity V and an angular velocity about the center- of-mass + cm....
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