OLDHW26 - oldhomewk 26 PAPAGEORGE MATT Due Apr 1 2008 4:00...

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oldhomewk 26 – PAPAGEORGE, MATT – 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 ℓ 2. L = parenleftbigg M m M + m parenrightbigg v ℓ 3. L = ( M - m ) v ℓ 4. L = ( m + M ) v ℓ 5. L = m v ℓ correct Explanation: Basic Concepts: If summationdisplay vector τ 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 = m v ℓ . 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 = 2 m m + M 2. K f K i = m m + M correct 3. K f K i = 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 m v ℓ = ( m + M ) v f ℓ . Therefore v f = v parenleftbigg m m + M parenrightbigg K i = 1 2 m v 2 K f = 1 2 I ω 2 f where I = ( M + m ) 2 and ω 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 m v 2 = m M + m . Question 3, chap 13, sect 3. part 1 of 2 10 points A small puck of mass 49 g and radius 48 cm slides along an air table with a speed of 2 . 1 m / s. It makes a glazing collision with a
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oldhomewk 26 – PAPAGEORGE, MATT – Due: Apr 1 2008, 4:00 am 2 larger puck of radius 74 cm and mass 76 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 m r 2 . + ω + ω 2 . 1 m / s V cm 49 g 76 g (a) (b) (c) 74 cm 48 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 ω about the center- of-mass “+ cm”. What is the angular momentum of the sys- tem relative to the center of mass after the collision?
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