Concept explainers
(a)
The velocities of each car if A and C hits B at the same time.
Answer to Problem 13.162P
Explanation of Solution
Given information:
Mass of each bumper car is equal to
Riders A, B and C have mass of
The total linear momentum of two particles is conserved. Therefore,
The co-efficient of restitution is defined as:
Calculation:
The mass of each bumper car with riders:
Apply conservation of linear momentum for all 3 bumper cars:
Substitute,
The co-efficient of restitution for A and B:
Substitute,
The co-efficient of restitution for B and C,
Substitute,
By solving equations 1,2 and 3,
Conclusion:
The velocities of each car are calculated by solving equations 1, 2 and 3.
(b)
The velocities of each car if A hits B before C does.
Answer to Problem 13.162P
Explanation of Solution
Given information:
Mass of each bumper car is equal to
Riders A, B and C have mass of
The total linear momentum of two particles is conserved. Therefore,
The co-efficient of restitution is defined as,
Calculation:
The mass of each bumper car with riders,
Apply conservation of linear momentum for A and B,
Substitute,
The co-efficient of restitution for A and B,
Substitute,
Solve equations 1 and 2,
For the second impact,
Apply conservation of linear momentum for A and B,
Substitute,
The co-efficient of restitution for A and B,
Substitute,
Solve above equations,
For the third impact,
Apply conservation of linear momentum for A and B,
Substitute,
The co-efficient of restitution for A and B,
Substitute,
Solve equations 3 and 4,
Therefore, the final velocities are,
Conclusion:
The velocities of all 3 cars after, car A hits B before C does,
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Chapter 13 Solutions
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