A 300-g block is dropped onto a vertical spring with springconstant k =130.0 N/m

Question

A 300-g block is dropped onto a vertical spring with springconstant k =130.0 N/m. The block becomes attached to thespring, and the spring compresses 31.7 cm beforemomentarily stopping. While the spring is being compressed, whatwork is done on the block by its weight? The work is .93J While the spring is being compressed, the work on the block bythe spring force is -6.52J. The Speed of the block just before it hits thespring,(assuming that friction is negligible). is 6.10m/s I cant find, If thespeed at impact is doubled, what is the maximum compression of thespring? A 300-g block is dropped onto a vertical spring with springconstant k =130.0 N/m. The block becomes attached to thespring, and the spring compresses 31.7 cm beforemomentarily stopping. While the spring is being compressed, whatwork is done on the block by its weight? The work is .93J While the spring is being compressed, the work on the block bythe spring force is -6.52J. The Speed of the block just before it hits thespring,(assuming that friction is negligible). is 6.10m/s I cant find, If thespeed at impact is doubled, what is the maximum compression of thespring?

Explanation / Answer

(a)    from the given problem the cvompression of thespring is 31.7 cm = 0.317 m    so the workdone by the force of gravity willbe    W1 = m g d          = (0.300kg) (9.80 m / s2) (0.317 m)          = ........J (b)    the work done by the spring will be    W2 = (1 / 2) kd2          = (1 /2) (130 N / m) (0.317 m)2          =.........J (c)    for this we use the work energy theorem whichgives    KE = 0 - (1 / 2) mvi2            = W1 + W2    so the speed of the block just before ithits the spring will be    vi = [(- 2) (W1 +W2) / m]        = ........ m /s (d)    let the new speed after it has doubled isvi'    then again by using work energty theorem weget        0 - (1 / 2) m vi'2 = mg d' - (1 / 2) k d'2    d' = m g + [(m2 g2)+ (m k vi'2)]        = ....... m    d' = m g + [(m2 g2)+ (m k vi'2)]        = ....... m

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