COLLEGE PHYSICS,VOLUME 1
COLLEGE PHYSICS,VOLUME 1
2nd Edition
ISBN: 9781319115104
Author: Freedman
Publisher: MAC HIGHER
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Chapter 7, Problem 72QAP
To determine

(a)

Which would make the block swing higher, a 0.204 Ruger bullet of mass 2.14 g and muzzle speed 1290 m/s or a 7 mm Remington Magnum bullet of mass 9.71 g and muzzle speed 948 m/s? Assume the bullets enter the block right after leaving the muzzle of the rifle?

Expert Solution
Check Mark

Answer to Problem 72QAP

Remington bullet will make the block swing higher.

Explanation of Solution

Given info:

  mRuger=2.14gvRuger=1290m/smRemington=9.71gvRemington=948m/s

Formula used:

Calculation:

By conservation of momentum,

  mbulletvix=(mbullet+mblock)vfxvfx=mbulletvix(mbullet+mblock)

By conservation of energy,

  12(mbullet+mblock)v2fx=(mbullet+mblock)ghh=v2fx2g=12g( m bullet m bullet + m block )2v2ix

We know that mbullet<<<mblock

So, we have,

  h=v2ix2g( m bullet m block)2

Comparing the height of 2 bullets,

  hRugerhRemington=[ v 2 ix 2g ( m bullet m block )2]Ruger[ v 2 ix 2g ( m bullet m block )2]Remington=[v2 ixm bullet2]Ruger[v2 ixm bullet2]Remington=12902×2.1429482×9.712=0.090

Here the ratio is less than 1, so the Remington bullet will make the block swing higher.

Conclusion:

Remington bullet will make the block swing higher.

To determine

(b)

Using your answer in part (a), the mass of the block so that when hit by the bullet it will swing through a 60.0° angle? The block hangs from wire of length 1.25 m and negligible mass.

Expert Solution
Check Mark

Answer to Problem 72QAP

Mass of block = 2.62 kg

Explanation of Solution

Given info:

Formula used:

Calculation:

From trigonometry the final height of block reached is,

  h=LLcos60

By conservation of energy,

  12(mbullet+mblock)v2fx=(mbullet+mblock)ghvfx=2gh=2g(LLcos60)

By conservation of momentum,

  mbulletvix=(mbullet+mblock)vfxmblock=mbulletvixmbulletvfxvfx=mbulletvixmbullet2g(LLcos60)2g(LLcos60)mblock=mbulletvixmbulletgLgL=9.71×9489.71×9.81×1.259.81×1.25=2620g=2.62kg

Conclusion:

Mass of block = 2.62 kg

To determine

(c)

What is the speed of an 8.41-g bullet that causes the block to swing upward through a 30.0° angle?

Expert Solution
Check Mark

Answer to Problem 72QAP

Speed of an 8.41-g bullet = 566 m/s

Explanation of Solution

Given info:

Formula used:

Calculation:

From trigonometry the final height of block reached is,

  h=LLcos30

By conservation of energy,

  12(mbullet+mblock)v2fx=(mbullet+mblock)ghvfx=2gh=2g(LLcos30)

By conservation of momentum,

  mbulletvix=(mbullet+mblock)vfxvix=(mbullet+mblock)vfxmbullet=(mbullet+mblock)2g(LLcos30)mbulletvix=(8.41+2620)2×9.81(1.251.25cos30)8.41=566m/s

Conclusion:

Speed of an 8.41-g bullet = 566 m/s

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COLLEGE PHYSICS,VOLUME 1

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