(a) What is the speed of the cork if it isreleased as the spring passes through
ID: 1674975 • Letter: #
Question
(a) What is the speed of the cork if it isreleased as the spring passes through its relaxed position?1 m/s
(b) Suppose, instead, that the cork sticks to the spring andstretches it 1.5 cm before separation occurs. What now is the speedof the cork at the time of release?
2 m/s (a) What is the speed of the cork if it isreleased as the spring passes through its relaxed position? 1 m/s (b) Suppose, instead, that the cork sticks to the spring andstretches it 1.5 cm before separation occurs. What now is the speedof the cork at the time of release? 2 m/s Figure (a) applies to the spring in a cork gun (Figure(b)); it shows the spring force as a function of thestretch or compression of the spring. The spring is compressed by5.5 cm and used to propel a 3.8 g corkfrom the gun.
Explanation / Answer
Force constant of thespring = force /compression = slopeof graph = {0.4- ( -0.4)} / {4 - ( -4)} * 10-2 = 0.8/ 8 * 10-2 = 10 N/m Energy stored inspring U = (1/2)* k * x2 = 0.5* 10 * (5.5 * 10-2)2 = 1.51* 10-2 J a. According to law ofconservation of energy, K.E. of cork at realesepoint (1/2) * m *v12 = U 0.5 *3.8 * 10-3 *v12 = 1.51* 10-2 v1 = (1.51* 10-2 / 1.9 * 10-3) = 2.82 m/s v1 = (1.51* 10-2 / 1.9 * 10-3) = 2.82 m/s b. If the spring isstretched by x1 m, then (1/2) *m *v22 = U - (1/2)* k * x12 = 1.51* 10-2 - 0.5 * 10 *(1.5 * 10-2)2 = 1.397* 10-2 J v2 = (1.397* 10-2 / 1.9 * 10-3) = 2.71 m/s = 1.397* 10-2 J v2 = (1.397* 10-2 / 1.9 * 10-3) = 2.71 m/sRelated Questions
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