Concept explainers
(a)
The velocity of the particles.
(a)
Answer to Problem 69P
The velocity of the particles is
Explanation of Solution
Write the expression from conservation of momentum.
Here,
Write the equation for initial momentum.
Here,
Write the equation for final momentum at the distance of closest approach.
Here,
Rewrite the expression from equation (I) by using (II), (III) in terms of final velocity.
Conclusion:
Substitute,
Thus, the velocity of the particles is
(b)
The closest distance.
(b)
Answer to Problem 69P
The closest distance is
Explanation of Solution
Here, initial potential energy is zero.
Write the expression from conservation of energy.
Here,
Write the equation for initial kinetic energy.
Write the equation for final kinetic energy.
Write the equation for final potential energy.
Here,
Rewrite the expression from equation (V) by using (VI), (VII) and (VIII) in terms of distance.
Conclusion:
Substitute,
Thus, the closest distance is
(c)
The velocity of first particle.
(c)
Answer to Problem 69P
The velocity of first particle is
Explanation of Solution
The initial velocity of second particle is zero.
Write the expression from relative velocity equation.
Rewrite the expression from equation (IV) by using (X) in terms of final velocity of first particle.
Conclusion:
Substitute,
Thus, the velocity of first particle is
(d)
The velocity of second particle.
(d)
Answer to Problem 69P
The velocity of second particle is
Explanation of Solution
Write the expression from relative velocity equation.
Conclusion:
Substitute,
Thus, the velocity of second particle is
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Chapter 20 Solutions
Principles of Physics: A Calculus-Based Text
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