consider a bullet (mass =2.3g velocity=250m/s) fired into a large stationary blo

Question

consider a bullet (mass =2.3g velocity=250m/s) fired into a large stationary block of wood (mass=1.0kg) which is sitting on a frictionless surface and attached to an ideal spring (spring constant=5N/m).

Assume that the bullet is fired horizontally and that the collision occurs rapidly enough that the block does not move during the collision.

Find the speed of the bullet and block after the collision assuming they stick together.

Find the fraction of kinetic energy lost in the collision.Using your answer to part 1, find the maximum distance the spring is compressed assuming that you can ignore all non-conservative forces after the collision.

Explanation / Answer

Part A

By conservation of linear momentum

m1v1+m2v2+ (m1+m2)V

0.0023 * 250 + 0 = (0.0023+1)V

V = 0.573m/s

Part B

kinetiv energy lost

KE = 1/2m1*v1^2 - 1/2(m1+m2)V^2

KE = 0.5*0.0023*250.250 - 0.5*(0.0023+1)*0.573*0.573

KE = 71.875 - 0.1645

KE = 71.71

fraction = 71.71/71.875 = 0.99

Part C

spring is compresed by x then

1/2k*x^2 = 1/2(m1+m2)V^2

0.5*5*x^2 = 0.1645

x = 0.25m

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