This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 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 ℓ 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 ℓ What is the angular momentum L of the blockbullet 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 = mv 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 = mv 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 mv ℓ = ( m + M ) v f ℓ. Therefore v f = v parenleftbigg m m + M parenrightbigg K i = 1 2 mv 2 K f = 1 2 I ω 2 f where I = ( M + m ) ℓ 2 and ω f = v f ℓ . 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 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 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 mr 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 centerof mass has a linear velocity V and an angular velocity ω about the center ofmass “+ cm”....
View
Full Document
 Spring '09
 KLEINMAN
 Physics, Angular Momentum, Mass, MATT –

Click to edit the document details