You have been asked to design a \"ballistic spring system\" to measure the speed

Question

You have been asked to design a "ballistic spring system" to measure the speed of bullets. A bullet of mass m is fired into a block of mass M. The block, with the embedded bullet, then slides across a frictionless table and collides with a horizontal spring whose spring constant is k. The opposite end of the spring is anchored to a wall. The spring's maximum compression d is measured.

*I just need help with Part C the other parts are complete and correct*

Part A

Part complete

Find an expression for the bullet's initial speed vB in terms of m, M, k, and d.

Express your answer in terms of the variables m, M, k, and d.

dmk(m+M)???????????

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Correct

Part B

Part complete

What was the speed of a 1.7 g bullet if the block's mass is 1.0 kg and if the spring, with k = 21 N/m , was compressed by 12 cm ?

Express your answer using two significant figures.

320

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Correct

Part C

What percentage of the bullet's energy is "lost"?

Enter your answer to four significant figures.

SubmitRequest Answer

dmk(m+M)???????????

Explanation / Answer

(A) after collision Applying energy conservation,

(M + m) v^2 / 2 = k d^2 /2

v = sqrt[ k / (M + m)] d

Applying momentum conservation,

pi = pf

m vB = (M + m) v

m vB = sqrt[ k (M + m)] d

vB = ( d / m) sqrt[ k ( M + m)]

(B) vB = (0.12 / 0.0017) sqrt(21 (1 + 0.0017))

vB =324 m/s ......Ans

(C) Ki = (0.0017) (324^2)/2 = 89.1 J

final energy , Kf = k d^2 /2 = 21 (0.12^2) /2

Kf = 0.1512 J

K_lost = Ki - kf = 88.95 J  

% lost = (88.95 / 89.1)(100) = 99.8 %

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