A 1600-kg car traveling due east with a speed of 30 m/s collides head-on with a 4800-kg truck traveling due west with a speed of 15 m/s. The two vehicles stick together after the collision.
- a. What is the total momentum of the system prior to the collision?
- b. What is the velocity of the two vehicles just after the collision?
- c. What is the total kinetic energy of the system before the collision?
- d. What is the total kinetic energy just after the collision?
- e. Is the collision elastic? Explain.
(a)
The total momentum of the system prior to the collision.
Answer to Problem 5SP
The total momentum of the system prior to the collision is
Explanation of Solution
Given info: The mass of the car is
Write the expression for total momentum of the system prior to the collision.
Here,
Substitute
Conclusion:
Therefore, the total momentum of the system prior to the collision is
(b)
The velocity of the two vehicles just after the collision.
Answer to Problem 5SP
The velocity of the two vehicles just after the collision is
Explanation of Solution
Write the expression to find the velocity of the two vehicles just after collision.
Substitute
Conclusion:
Therefore, the velocity of the two vehicles just after the collision is
(c)
The total kinetic energy of the system before collision.
Answer to Problem 5SP
The total kinetic energy of the system before collision is
Explanation of Solution
Write the expression to find the kinetic energy of the system before collision.
Here,
Substitute
Conclusion:
Therefore, the total kinetic energy of the system before collision is
(d)
The total kinetic energy of the system just after collision.
Answer to Problem 5SP
The total kinetic energy of the system just after collision is
Explanation of Solution
Write the expression to find the total kinetic energy of the system just after collision.
Here,
Substitute
Conclusion:
Therefore, the total kinetic energy of the system just after collision is
(e)
Whether the collision is elastic.
Answer to Problem 5SP
No, the collision is not elastic.
Explanation of Solution
Elastic collision associates with it no change in the kinetic energy, that means for an elastic collision to occur, there should be no change in the kinetic energy before and after collision should be same.
When the vehicles stick together after collision, the kinetic energy before and after collision are the same. This results in inelastic collision case. Thus the head on collision of a car and truck is in elastic in nature since after the collision, they stick together.
Conclusion:
Therefore, the collision is not elastic.
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Chapter 7 Solutions
Physics of Everyday Phenomena
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