(a) What is the speed of the cork if it isreleased as the spring passes through

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/s                                     

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