(706) Problem 15: A massless spring (with force constant k= 198 N/m) connects a

Question

(706) Problem 15: A massless spring (with force constant k= 198 N/m) connects a wall and a block of wood. The system is initially at rest, with the spring unstretched The block has mass M= 50.1 g and is able to move without friction on a table. A gun is positioned to fire a bullet of mass in = 5.5 g into the block along the spring axis. After the gun is fired, the bullet gets embedded in the block, and the spring is compressed a maximum distance d 0.99 m ©theexpert ta.com 5000 Part (a) Find an equation for the speed of the bullet v. Just before it hits the block, in terms of the variables given in the problem statement > 5096 Part (b) In meters per second, what is the speed of the bullet v before it enters the block? Grade Summary Potential 100% sin0) cotan si acosO atanacotan sinhO cosh tanh cotanhO tan() | Submissions Attempts remaining: 10 (000 per attempt) detailed view coso 0 END Degrees Radians N( DEL CLEAR Submit Hint I give up! Hints: 0% deduction per hint. Hints remaining: 1 Feedback: deduction per feedback.

Explanation / Answer

(A) Applying energy conservation after collision,

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

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

Now applying momentum conservation for the collsion,

m v0 + 0 = (m + M) v

v0 = (M + m)/m0 ) (sqrt[ k / (M + m)] d )

v0 = sqrt[ k (M + m)] (d /m)

(B) putting values,

v0 = sqrt[ 198 (0.0501 + 0.0055)] (0.99 / 0.0055)

v0 = 597 m/s  

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