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(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/s