Answered: 6) A massless spring, with force…

Name: 6) A massless spring, with force constant k=191N/m, connects a wall an
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Description: 6) A massless spring, with force constant k=191N/m, connects a wall and a block of wood. The system is initially at rest with the spring neither stretched nor compressed. The block has mass M=54.2g and is free to move without friction on a table. A g

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter8: Momentum And Collisions

Section: Chapter Questions

Problem 57P: A 5.00-g bullet moving with an initial speed of v = 400 m/s is fired into and passes through a...

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6) A massless spring, with force constant k=191N/m, connects a wall and a block of wood. The system is initially at rest with the spring neither stretched nor compressed. The block has mass M=54.2g and is free to move without friction on a table. A gun is positioned to fire a bullet of mass m=6.86g 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=0.857m.

b) What is the speed, in meters per second, of the bullet before it enters the block?

c) What is the frequency, in hertz, of the resulting periodic motion of the block/bullet and spring system?

Expert Solution

Step 1

Write the momentum conservation equation.

$\begin{array}{l} m u_{1} + M u_{2} = (m + M) v \\ m u_{1} + M (0) = (m + M) v \\ v = (\frac{m}{m + M}) u_{1} \end{array}$

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