Question

A bullet of mass M is fired from a gun of mass M.The recoiling gun compress a spring of force constannt K by a distance D.The vilocity of the bullet is

Answer 1

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Answer 2

Given:

Mass of the bullet = m

Mass of the gun = M

Spring constant = K

Distance moved by the spring = D

To find: The velocity of the bullet v

Formula Used:

The potential energy stored in the spring is  $W=\frac{1}{2}kx^2$

Kinetic energy stored in an object = $K=\frac{1}{2}m(v^2-u^2)$

Calculations:

Initial velocity of gun and bullet = 0

The final velocity of the gun can be calculated as follows:

$\frac{1}{2}KD^2=\frac{1}{2}MV^2\\V=\sqrt \frac{K}{M}D$

Use Law of conservation of momentum to find the velocity of the bullet:

$mv+MV = mu+MU\\mv+MV=0\\mv=-MV\\v=-\frac{M}{m}\sqrt \frac{K}{M}D\\v=-\frac {D}{m}\sqrt{KM}$

Learn more about: Law of conservation of momentum

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