Review Conceptual Example 8 before starting this problem. A block is attached to

Question

Review Conceptual Example 8 before starting this problem. A block is attached to a horizontal spring and oscillates back and forth on a frictionless horizontal surface at a frequency of 4.19 Hz. The amplitude of the motion is 3.77 x 10-2 m. At the point where the block has its maximum speed, it suddenly splits into two identical parts, only one part remaining attached to the spring. (a) What is the amplitude and (b) the frequency of the simple harmonic motion that exists after the block splits? (a) Number Units (b) Number Units

Explanation / Answer

(a) kAnew2/2 = (m/2)vmax2/2 = kA2/4

=> new amplitude, Anew = A / 21/2 = 3.77 * 10-2 / 21/2 = 2.66 * 10-2 m

(b) New frequency, fnew = (1/2)[k / (m/2)]1/2 = f * 21/2 = 4.19 * 21/2 = 5.93 Hz

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