A spring gun is made by compressing a spring in a tube and then latching the spr

Question

A spring gun is made by compressing a spring in a tube and then latching the spring at

the compressed position. A 4.97-g pellet is placed against the compressed and latched

spring. The spring latches at a compression of 4.76 cm, and it takes a force of

9.12 N to compress the spring to that point.

(a) If the gun is fired vertically, how fast (m/s) is the pellet moving when it loses contact

with the spring?

(b) To what maximum height (m) will the pellet rise? (as measured from the original

latched position)

Explanation / Answer

a)

k = F/x = 9.12/0.0476 = 191.6

conservation of energy:

0.5 k x^2 = m g x + 0.5 m v^2

==> 0.5*191.6*0.0476*0.0476 = 4.97e-3*9.8*0.0476 + 0.5*4.97e-3*v^2

==> v = 9.30 m/s

b)

conservation of energy:

0.5 k x^2 = m g h

==> 0.5*191.6*0.0476*0.0476 = 4.97e-3*9.8*h

==> h = 4.46 m

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