8) A block of unknown mass is attached to a spring with aspring constant of 5.00
ID: 1673847 • Letter: 8
Question
8) A block of unknown mass is attached to a spring with aspring constant of 5.00 N/m and undergoessimple harmonic motion with an amplitude of 11.0 cm. When the block is halfway between itsequilibrium position and the end point, its speed is measured to be28.0 cm/s. (a) Calculate the mass of the block.________________ kg
(b) Calculate the period of the motion.
_________________ s
(c) Calculate the maximum acceleration of the block.
_________________ m/s2 (a) Calculate the mass of the block.
________________ kg
(b) Calculate the period of the motion.
_________________ s
(c) Calculate the maximum acceleration of the block.
_________________ m/s2
Explanation / Answer
Amplitude A = 11.0 cm = 0.11 m springconstant k = 5.00 N/m Speed at y = A /2, v0.055 = 28cm/s = 0.28 m/s a. Speed of block atposition y is given by vy2 = 2*(A2 - y2) Substituting y = A/2 v0.0552 = 2*(A2 - A2/4) 3 *0.112 * 2 /4 = 0.282 2 = 0.282* 4 / 0.112 * 3 = 12.96 = 12.96 = 3.60 rad/s also 2 = k/ m => m = k/ 2 = 5.00/ 12.96 = 0.356 kg = 5.00/ 12.96 = 0.356 kg b. Timeperiod T = 2/ = 2* 3.14 / 3.60 = 1.74 s c. maximumaccerleration = -2 * A = -12.96 * 0.11 = -1.4256 m/s2 - ve sign indicates that the acceleration isdirected towards the equilibrium position. - ve sign indicates that the acceleration isdirected towards the equilibrium position.Related Questions
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