Concept explainers
(a)
The
(a)
Answer to Problem 41P
Yes, the bullet has angular momentum about the door fixing axis.
Explanation of Solution
Write the expression for angular momentum for an object as.
Here,
Force acting on the door-bullet system as shown below.
Conclusion:
Yes, the bullet has angular momentum about the door. The value of angular momentum for bullet will be the product of the moment of inertia of bullet and the angular speed of the bullets.
Thus, yes the bullet has angular momentum about the door fixing axis.
(b)
The angular momentum for bullet relative to the door’s axis of rotation.
(b)
Answer to Problem 41P
The angular momentum for bullet relative to the door’s axis of rotation is
Explanation of Solution
Conclusion:
Substitute
Thus, the angular momentum for bullet relative to the door’s axis of rotation is
(c)
The mechanical energy of the bullet– door system during this collision.
(c)
Answer to Problem 41P
The mechanical energy of the bullet-door system during this collision will not remain constant.
Explanation of Solution
Conclusion:
The collision of bullet and door is an inelastic collision; therefore, the mechanical energy of the bullet door system will not remain constant during a collision. In an inelastic collision, there is high friction between bullet and door so the amount of mechanical energy or kinetic energy of the bullet converts into internal energy of the bullet door system.
Thus, the mechanical energy of the bullet-door system during this collision will not remain constant.
(d)
The angular speed at which the door swing open immediately after the collision.
(d)
Answer to Problem 41P
The angular speed at which the door swing open immediately after the collision is
Explanation of Solution
Write the expression for moment of inertia of a bullet as.
Here,
Write the expression for moment of inertia for a stick or thin rod when it pivoted at another end as.
Here,
Write the expression for total moment of inertia which is the sum of MOI’s of door and bullet as.
Write the expression for total angular momentum as.
Here,
For conservation of angular momentum, equate the angular momentum of the bullet to the final angular momentum of door and bullet mass system as.
Conclusion:
Substitute
Simplify the above expression for
Thus, the angular speed at which the door swing open immediately after the collision is
(e)
The kinetic energy of the door-bullet system immediately after impact.
(e)
Answer to Problem 41P
The kinetic energy of the door-bullet system immediately after impact
Explanation of Solution
Write the expression for rotational kinetic energy as.
Here,
Write the expression for kinetic energy for the bullet as.
Here,
Substitute
Conclusion:
Substitute
Substitute
Thus, the kinetic energy of the door-bullet system immediately after impact
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Chapter 11 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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