Question

You fire a 50-g arrow that moves at an unknown speed. it hits and embers in a 350-g block that slides on an air track. at the end, the block runs into and compresses a 4000-n/m spring 0.10 m. how fast was the arrow traveling? indicate the assumptions you make and how they affect your results.

Answer 1

The solution for this problem is:

 

Work it backwards: spring U = ½kx² = ½ * 4000N/m * (0.10m) ² = 20 J 

so the pre-impact of KE = 20 J = ½ * m * v² = ½ * 0.40kg * v² 

v = 10 m/s → for the bullet/block. 

Now conserve the momentum: 

50g * u = 400g * 10m/s 

u = 80 m/s is the arrow velocity