(a)
The reason that why the successful tackle constitutes a perfectly inelastic collision.
(a)
Answer to Problem 30P
The successful tackle constitutes a perfectly inelastic collision because they are stuck together and the momentum is conserved.
Explanation of Solution
Given info: The mass of the fullback is
Momentum is a vector quantity which is always conserved in a closed system while kinetic energy is not a vector quantity. So, it is use the direction and magnitude of the player’s original momenta to figure out how they will be moving post collision. Thus, the successful tackle constitutes a perfectly inelastic collision because they are stuck together and the momentum is conserved.
Conclusion:
Therefore, the successful tackle constitutes a perfectly inelastic collision because they are stuck together and the momentum is conserved.
(b)
The velocity of the players immediately after the tackle.
(b)
Answer to Problem 30P
The velocity of the players immediately after the tackle is
Explanation of Solution
Given info: The mass of the fullback is
Formula to calculate the momentum of the fullback is,
Here,
Substitute
Thus, the momentum of the fullback is
Formula to calculate the momentum of the opponent is,
Here,
Substitute
Thus, the momentum of the opponent is
After the collision, the momentum of the players will be neither be in north nor in east.
It should be in between north and east. So, the addition of vectors is used to calculate the momentum of the players immediately after the tackle.
Formula to calculate the hypotenuse of right triangle formed by placing the vectors is,
Here,
Substitute
Thus, the momentum of the players immediately after the tackle is
Formula to calculate the combined mass of the players is,
Here,
Substitute
Thus, the combined mass of the players is
Formula to calculate the velocity of the players immediately after the tackle is,
Here,
Substitute
Conclusion:
Therefore, the velocity of the players immediately after the tackle is
(c)
The decrease in the mechanical energy as a result of the collision.
(c)
Answer to Problem 30P
The decrease in the mechanical energy as a result of the collision is
Explanation of Solution
Given info: The mass of the fullback is
Formula to calculate the kinetic energy of the fullback is,
Here,
Substitute
Thus, the kinetic energy of the fullback is
Formula to calculate the kinetic energy of the opponent is,
Here,
Substitute
Thus, the kinetic energy of the opponent is
Formula to calculate the total kinetic energy of the player prior to the collsion is,
Here,
Substitute
Thus, the total kinetic energy of the player prior to the collsion is
Formula to calculate the total kinetic energy followed by the collision is,
Here,
Substitute
Thus, the total kinetic energy followed by the collision is
Formula to calculate the decrease in the mechanical energy as a result of the collision is,
Here,
Substitute
This decrease in the mechanical energy as a result of the collision is converted into heat energy to tackle.
Conclusion:
Therefore, the decrease in the mechanical energy as a result of the collision is
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Chapter 8 Solutions
Principles of Physics: A Calculus-Based Text, Hybrid (with Enhanced WebAssign Printed Access Card)
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