6) A spring is hung from the ceiling. A 0.600-kg block is then attached to the f

Question

6) A spring is hung from the ceiling. A 0.600-kg block is then attached to the free end of the spring. When released from rest, the block drops 0.110 m before momentarily coming to rest, after which it moves back upward. (a) What is the spring constant of the spring? (b) Find the angular frequency of the block's vibrations. 8) A heavy-duty stapling gun uses a 0.123 kg metal rod that rams against the staple to eject it. The rod is attached and pushed by a stiff spring called a "ram spring" (k = 32664 N/m). The mass of this spring may be ignored. Squeezing the handle of the gun first compresses. The ram spring is compressed by 3.20 10-2 m from its unstrained length and then releases from rest. Assuming that the ram spring is oriented vertically and is still compressed by 1.17 10-2 m when the downward-moving ram hits the staple, find the speed of the ram at the instant of contact.

Explanation / Answer

6) A spring is hung from the ceiling. A 0.600-kg block is then attached to the free end of the spring. When released from rest, the block drops 0.110 m before momentarily coming to rest, after which it moves back upward.

(a) What is the spring constant of the spring?

k * 0.110/2 = m g

k = 0.6*9.8*2/0.110 = 106.91 = 107 N/m

(b) Find the angular frequency of the block's vibrations.

w = sqrt(k/m) = sqrt(106.91/0.6) = 13.3 rad/s

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