A spring gun is mounted on a lab table such that its muzzle is level with the su

Question

A spring gun is mounted on a lab table such that its muzzle is level with the surface of the table and pointed up into the air. A bullet with mass 55.0 g is loaded into the spring gun, compressing the spring by 9.00 cm. When the trigger is pressed, the bullet shoots out vertically into the air, reaches a maximum height and falls back down, striking the surface of the table after a total flight of 4.00 seconds. Use g = 9.80 m/s2. a. Assuming all the energy stored in the spring is transferred to the ball, determine the spring constant of the spring.

Explanation / Answer

We need to first determine the velocity of the bullet out of the muzzle

y=(g/2)t2+vt

0=(-9.8/2)(4)2+v(4)

v=19.6 m/s

Now we relate this as kinetic energy to the potential energy of the spring

KE=PE

(1/2)mv2=(1/2)kx2

(1/2)(.055)(19.6)2=(1/2)k( .09)2

k=2608.5 N/m

hope that helps

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