A 240 g block is dropped onto a relaxed vertical spring that hasa spring constan

Question

A 240 g block is dropped onto a relaxed vertical spring that hasa spring constant of k = 1.9 N/cm (Fig. 7-43). The blockbecomes attached to the spring and compresses the spring 14 cmbefore momentarily stopping. While the spring is being compressed,what work is done on the block by (a) thegravitational force on it and (b) the springforce? (c) What is the speed of the block justbefore it hits the spring? (Assume that friction is negligible.)(d) If the speed at impact is doubled, what is themaximum compression of the spring?

Explanation / Answer

(a)    from the given problem the cvompression of thespring is 14 cm = 0.14 m    so the workdone by the force of gravity willbe    W1 = m g d          = (0.240kg) (9.80 m / s2) (0.14 m)          = ........J (b)    the work done by the spring will be    W2 = (1 / 2) kd2          = (1 /2) (190 N / m) (0.14 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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