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Homework 8

Homework 8 - Solution for Long-answer Homework 8 Energy...

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Solution for Long-answer Homework 8 Energy problems Solution to Long-answer Homework Problem 8.1() Problem: A car with inertia 1200kg is backing out of a parking space at 5 m s . An unobservant driver of a 1800kg pickup truck is coasting through the parking lot at a speed of 3 m s , and runs straight into the rear bumper of the car. (a)What is the change in internal energy of the system, if the speed of the pickup is 1 . 5 m s backwards after they collide? (b)What is the coefficient of restitution for this collision? Solution to Part (a) Conserving momentum: m c v c,i + m t v t,i = m c v c,f + m t v t,f v c,f = m c v c,i + m t ( v t,i - v t,f ) m c v c,f = (1200kg) ( - 5 m s ) + (1800kg) ( 3 m s - ( - 1 . 5 m s )) 1200kg v c,f = 1 . 75 m s Energy is conserved, so Δ E + Δ K = 0 Δ E = - Δ K = K i - K f = 1 2 m c ( v 2 c,i - v 2 c,f ) + 1 2 m t ( v 2 t,i - v 2 t,f ) Δ E = 1 2 (1200kg) parenleftbigg parenleftBig - 5 m s parenrightBig 2 - parenleftBig 1 . 75 m s parenrightBig 2 parenrightbigg + 1 2 (1800kg) parenleftbigg parenleftBig 3 m s parenrightBig 2 - parenleftBig - 1 . 5 m s parenrightBig 2 parenrightbigg Δ E = 19237 . 5J Notice this is positive, which means the internal energy of the system increases during the collision. Grading Key: Part (a) 3 Points Solution to Part (b) The coefficient of restitution is given by: e = - v rel,f v rel,i So e = - v c,f - v t,f v c,i - v t,i = - 1 . 75 m s - ( - 1 . 5 m s ) - 5 m s - 3 m s e = 0 . 40625 Grading Key: Part (b) 2 Points Total Points for Problem: 5 Points 1

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Solution to Long-answer Homework Problem 8.2(null)
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Homework 8 - Solution for Long-answer Homework 8 Energy...

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