#17

(6%) Problem 17: In the analysis of a block-spring system undergoing simple harmonic motion, the mass of the spring is usually considered negligible. However, when we do account for the mass of the spring, we find that its effect is to increase the period. Let the masses of the block and spring be M and m, respectively. Assume the spring is uniform and the speed of a slice of the spring is directly proportional to its distance from the fixed end. For example, the speeds of the spring at its fixed end, its mid-point, and the point where it connects to the block are 0, v/2, and v, respectively, where v is the instantaneous speed of the block. Forbes, David -.david.forbes@doane.edu @theexpertta.com - tracking id: 9N69-72-B9-45-AB7A-40022. In accordance with Expert TA's Terms of Service. copying this information to any solutions sharing website is strictly forbidden. Doing so may result in termination of your Expert TA Account. A 20% Part (a) Enter an expression for the kinetic energy of the spring in terms of m and v. K =1 Grade Summary Deductions 0% Potential 100% B Y 0 7 8 9 HOME Submissions b C d JA AL 4 5 6 Attempts remaining: 1 (100% per attempt) g h 2 3 detailed view k m n + 0 END P S V VO BACKSPACE CLEAR Submit Hint Feedback I give up! Hints: 0% deduction per hint. Hints remaining: 1 Feedback: 0% deduction per feedback. 4 20% Part (b) Calculate the kinetic energy, in joules, of a m = 0.065-kg spring in an oscillating block-spring system, when the block is moving at a speed of v = 1.8 m/s. 4 20% Part (c) Now write the kinetic energy of the spring as KE = 0.5mev, where v is the block's instantaneous speed and me is termed the effective mass of the spring. Enter an expression for me in terms of m and v. 4 20% Part (d) Calculate the effective mass, in kilograms, of an m = 0.065-kg spring in an oscillating block-spring system. 4 20% Part (e) Assume the mass in the formula for the period of oscillation of a block-spring system can be replaced by M + me. For M= 1.I kg and m = 0.065 kg by how much, in seconds, does the formula's value increase when the spring's effective mass is included in the calculation? Take a spring constant of k = 29 N/m. All content . 2023 Expert TA, LLC