Physics 101 Learning Object 1: Energy Conservation in Simple Harmonic Motion !

Image gathered from: http://homepages.spa.umn.edu/~yk/Image28.gif !!The above diagram shows 5 different mass-spring systems at different X distances, with all blocks with the same mass of 4kg. !!Question 1. In system (a), if distance X is -6cm, what is the total energy at that point? Choose the answer given in terms of k (constant) and v (velocity). A. 0 J B. 3k J C. 18k J D. -18k J E. 18k + 2v2 !Question 2. In system (c), with the distance of X=0cm, what is the total energy at that point? Choose the answer given in terms of k (constant) and v (velocity). ! A. 0 J B. 2v2 J C. 4kv2 J D. 4v2 J E. 8v2 J !

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Question 3. In system (d), when X=4cm, what is the total energy in terms of k (constant) and v (velocity)? ! A. 8k J B. 16k J C. 4v2 - 8k J D. 2v2 - 8k J E. 2v2 + 8k J !Question 4. In system (e), when X=6cm, what is the total energy in terms of k (constant) and v (velocity)? ! A. 36k J B. 18k J C. -18k J D. 18k + 2v2 J E. 36k + 2v2 J !Question 5. In all 5 of the systems, which system contains the most total energy? ! A. All systems have the same total energy. B. (c) C. (e) D. (a) E. Impossible to determine without more information. !!!!!!!!!!!!!

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Physics 101 Learning Object 1: Energy Conservation in Simple Harmonic Motion !

Image gathered from: http://homepages.spa.umn.edu/~yk/Image28.gif !!The above diagram shows 5 different mass-spring systems at different X distances, with all blocks with the same mass of 4kg. !!Question 1. In system (a), if distance X is -6cm, what is the total energy at that point? Choose the answer given in terms of k (constant) and v (velocity). A. 0 J B. 3k J C. 18k J D. -18k J E. 18k + 2v2 !Answer: C. Since total energy (X=-6, v=0) = K + U = (1/2)kX2 = (1/2)(-6)2k = 18k J !Question 2. In system (c), with the distance of X=0cm, what is the total energy at that point? Choose the answer given in terms of k (constant) and v (velocity). ! A. 0 J B. 2v2 J C. 4kv2 J

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D. 4v2 J E. 8v2 J !Answer: B. Total energy (X=0) = K + U = (1/2)mv2 = (1/2)(4)v2 = 2v2 J !Question 3. In system (d), when X=4cm, what is the total energy in terms of k (constant) and v (velocity)? ! A. 8k J B. 16k J C. 4v2 - 8k J D. 2v2 - 8k J E. 2v2 + 8k J !Answer: E. Total energy (X=4) = K + U = (1/2)mv2 + (1/2)kX2 = (1/2)(4)v2 + (1/2)(4)2k = 2v2 + 8k J !Question 4. In system (e), when X=6cm, what is the total energy in terms of k (constant) and v (velocity)? ! A. 36k J B. 18k J C. -18k J D. 18k + 2v2 J E. 36k + 2v2 J !Answer: B. Total energy (X=6, v=0) = K + U = (1/2)kX2 = (1/2)(6)2k = 18k J !Question 5. In all 5 of the systems, which system contains the most total energy? ! A. All systems have the same total energy. B. (c) C. (e) D. (a) E. Impossible to determine without more information. Answer: A. Due to the conservation of energy, all systems will have the same total energy with the formula E = K + U.

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