Thank you You have been asked to design a ballistic spring system to measure the

Question

Thank you You have been asked to design a ballistic spring system to measure the speed of bullets. A bullet of mass 5.0 g is fired into a block of mass 2.0 kg. The block, with the embedded bullet, then slides across a frictionless table and collides with a horizontal spring whose spring constant is 50 N/m. The opposite end of the spring is anchored to a wall. The spring's maximum compression is 10cm,. What is the speed of the bullet? Show complete equations that you use and state the physics principles that you use the problem. Explain your important steps in brief.

Explanation / Answer

Mass of the bullet m = 5 g = 0.005 kg

Mass of the block M = 2 kg

Let the speed of the bullet be v

Let the speed of the block be V1 = 0

Let the common velocity of the bullet and block be V

Here we know that momentum of the system is conserved

The kinetic energy of the bullet block system is transferred to spring

Let the spring constant k = 50 N/m

Compression be x = 10 cm = 0.1 m

So, 1/2 *(m + M) * V2 = 1/2 * k * x2

V2 = k * x2 / (m + M)

= 50 * 0.1 * 0.1 / (2 + 0.005)

= 0.5/2.005 = 0.24938

so, V = 0.49 m/s

Now we can substitute the value of common velocity v in equation for conservation of momentum

m * v + 0 = ( m + M ) * V

v = ( m + M ) * V / m

=( 0.005 + 2.0 ) * 0.49 / 0.005

= 196.5 m/s

So the velocity of the bullet is v = 196.5 m/s

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