Homework 20

# Homework 20 - homework 20 BAUTISTA, ALDO Due: Mar 20 2006,...

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Unformatted text preview: homework 20 BAUTISTA, ALDO Due: Mar 20 2006, 4:00 am 1 Version number encoded for clicker entry: V1:1, V2:4, V3:2, V4:4, V5:3. Question 1 Part 1 of 3. 10 points. Two small spheres of mass m 1 and m 2 are suspended from the ceiling at the same point by massless strings of equal length . The lighter sphere is pulled aside through an angle of i from the vertical and let go. The acceleration of gravity is 9 . 8 m / s 2 . g Before m 1 i m 2 g After f At what speed will the lighter mass m 1 hit the heavier mass m 2 ? 1. v 1 i = { 2 g [1- cos i ] } 2. v 1 i = { g [1- cos i ] } 1 2 3. v 1 i = { 2 g [cos i ] } 4. v 1 i = { g [cos i ] } 1 2 5. v 1 i = { 2 g [1- cos i ] } 1 2 correct 6. v 1 i = { g [1- cos i ] } 7. v 1 i = { 2 g [cos i ] } 1 2 8. v 1 i = { g [cos i ] } Explanation: The velocity just before the collision v i can be determined by energy conservation. When particle 1 is at its initial condition, it is at rest and displaced by an angle i from the vertical. The total energy is all potential and is given by U i = m 1 g (1- cos i ) where (1- cos i ) is the distance above the lowest point. Just before the collision, the en- ergy of sphere 1 is all kinetic energy, 1 2 m 1 v 2 1 i . Equating the two energies gives 1 2 m 1 v 2 1 i = m 1 g (1- cos i ) . Solving for v 1 i gives v 1 i = { 2 g [1- cos i ] } 1 / 2 . Question 2 Part 2 of 3. 10 points. After lighter sphere is let go and collides with the heavier sphere at the bottom of its swing, two spheres immediately bind to- gether. What is conserved in this collision process? Let E = mechanical energy; P = momentum. 1. Neither E nor P 2. E 3. Both E and P 4. P correct Explanation: This is a perfectly inelastic collision. The speed of the two spheres after collision is de- termined by momentum conservation. Question 3 Part 3 of 3. 10 points. After the lighter sphere is let go and col- lides with the heavier sphere at the bottom of homework 20 BAUTISTA, ALDO Due: Mar 20 2006, 4:00 am 2 its swing, the two spheres immediately bind together. What is the speed V f of the combined sys- tem just after the collision? 1. V f = m 1 + m 2 2 m 1 v 1 i 2. V f = m 2 m 1 + m 2 v 1 i 3. V f = m 1 + m 2 m 1 v 1 i 4. V f = 2 m 2 m 1 + m 2 v 1 i 5. V f = m 1 + m 2 m 2 v 1 i 6. V f = 2 m 1 m 1 + m 2 v 1 i 7. V f = m 1 m 1 + m 2 v 1 i correct 8. V f = m 1 + m 2 2 m 2 v 1 i Explanation: This is a completely inelastic collision. The speed of the two spheres after collision is de- termined by momentum conservation m 1 v 1 i = ( m 1 + m 2 ) V f (1) where m 1 is the mass and v 1 i is the initial velocity of sphere 1 just before the collision, m 2 is the mass of sphere 2, and V f is the velocity of the combined spheres just after the collision. Note: v 2 i = 0....
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## This note was uploaded on 10/13/2009 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas at Austin.

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Homework 20 - homework 20 BAUTISTA, ALDO Due: Mar 20 2006,...

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