Two bumper cars at the county fair are sliding toward one another (Fig. P11.54). Initially, bumper car 1 is traveling to the east at 5.62 m/s, and bumper car 2 is traveling 60.0° south of west at 10.00 m/s. After they collide, bumper car 1 is observed to be traveling to the west with a speed of 3.14 m/s. Friction is negligible between the cars and the ground. a. If the masses of bumper cars 1 and 2 are 596 kg and 625 kg respectively, what is the velocity of bumper car 2 immediately after the collision? b. What is the kinetic energy lost in the collision?
FIGURE P11.54 Problems 54 and 55.
(a)
Velocity of bumper car 2 after collision.
Answer to Problem 54PQ
Velocity of bumper car 2 after collision is
Explanation of Solution
Positive x axis points to the east and the positive y axis points to the north. Apply law of conservation of momentum. The momentum of cars before collision must be equal to the momentum of cars after collision.
Here,
Elaborate equation (I) in terms of mass and velocity.
Here,
Apply the same condition of conservation of momentum in the y direction also. Here only car 2 travels in the y direction.
The initial total momentum in the y direction is equal to the final momentum in the y direction.
Here,
Elaborate equation (III) in terms of mass and velocity.
Here,
Write the equation to find the final velocity of second car.
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, velocity of bumper car 2 after collision is
(b)
Kinetic energy lost during the collision.
Answer to Problem 54PQ
The kinetic energy lost is
Explanation of Solution
Write the equation to find the resultant final speed of car 2 after collision.
Here,
The kinetic energy lost is equal to the difference between the kinetic energy before collision and after collision.
Write the equation to find the kinetic energy lost.
Here,
Conclusion:
Substitute
Substitute
Therefore, the kinetic energy lost is
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Chapter 11 Solutions
Student Solutions Manual For Katz's Physics For Scientists And Engineers: Foundations And Connections, Volume 1
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