Homework 8 - Solutions

# Homework 8 - Solutions - homework 08 – FRENNEA KYLE –...

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Unformatted text preview: homework 08 – FRENNEA, KYLE – Due: Mar 23 2007, 5:00 am 1 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 ℓ . The lighter sphere is pulled aside through an angle of θ i from the vertical and let go. The acceleration of gravity is 9 . 8 m / s 2 . g Before m 1 ℓ θ i m 2 g After θ f At what speed will the lighter mass m 1 hit the heavier mass m 2 ? 1. v 1 i = { g ℓ [1- cos θ i ] } 1 2 2. v 1 i = { 2 g ℓ [cos θ i ] } 1 2 3. v 1 i = { 2 g ℓ [1- cos θ i ] } 4. v 1 i = { 2 g ℓ [cos θ i ] } 5. v 1 i = { g ℓ [cos θ i ] } 6. v 1 i = { g ℓ [1- cos θ i ] } 7. v 1 i = { g ℓ [cos θ i ] } 1 2 8. v 1 i = { 2 g ℓ [1- cos θ i ] } 1 2 correct 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 θ i from the vertical. The total energy is all potential and is given by U i = m 1 g ℓ (1- cos θ i ) where ℓ (1- cos θ 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 ℓ (1- cos θ i ) . Solving for v 1 i gives v 1 i = { 2 g ℓ [1- cos θ 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. Both E and P 2. E 3. P correct 4. Neither E nor P 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 its swing, the two spheres immediately bind together. homework 08 – FRENNEA, KYLE – Due: Mar 23 2007, 5:00 am 2 What is the speed V f of the combined sys- tem just after the collision? 1. V f = parenleftbigg m 1 + m 2 m 2 parenrightbigg v 1 i 2. V f = parenleftbigg m 1 + m 2 2 m 2 parenrightbigg v 1 i 3. V f = parenleftbigg 2 m 2 m 1 + m 2 parenrightbigg v 1 i 4. V f = parenleftbigg 2 m 1 m 1 + m 2 parenrightbigg v 1 i 5. V f = parenleftbigg m 2 m 1 + m 2 parenrightbigg v 1 i 6. V f = parenleftbigg m 1 + m 2 m 1 parenrightbigg v 1 i 7. V f = parenleftbigg m 1 m 1 + m 2 parenrightbigg v 1 i correct 8. V f = parenleftbigg m 1 + m 2 2 m 1 parenrightbigg 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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Homework 8 - Solutions - homework 08 – FRENNEA KYLE –...

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