Concept explainers
Review. From a large distance away, a particle of mass m1, and positive charge q1 is fired at speed υ in the positive x direction straight toward a second particle, originally stationary but free to move, with mass m2, and positive charge q2. Both particles are constrained to move only along the x axis. (a) At the instant of closest approach, both particles will be moving at the same velocity. Find this velocity, (b) Find the distance of closest approach. After the interaction, the particles will move far apart again. At this time, find the velocity of (c) the particle of mass m1, and (d) the particle of mass m2.
(a)
The velocity at the instant when the both particle moves with same velocity.
Answer to Problem 25.56AP
The velocity at the instant of closest approach when the both particle moves with same velocity is
Explanation of Solution
The initial velocity of the second particle is
The momentum is conserved of an isolated system.
Here,
Substitute
Conclusion:
Therefore, the velocity at the instant of closest approach when the both particle moves with same velocity is
(b)
The closet distance.
Answer to Problem 25.56AP
The closet distance is
Explanation of Solution
From part (a) the value of
Write the expression for initial the kinetic energy of first particle.
Here,
Write the expression for final the kinetic energy of first particle.
Here,
Write the expression for initial the kinetic energy of second particle.
Here,
Write the expression for final the kinetic energy of second particle.
Here,
Total initial kinetic energy is given by,
Substitute
Substitute
Total final kinetic energy is given by,
Substitute
The initial electric potential energy is
Here,
The final electric potential energy is expressed as,
Here,
The energy is conserved within the isolated system.
Substitute
Substitute
Conclusion:
Therefore, the closet distance is
(c)
The velocity of the particle of mass
Answer to Problem 25.56AP
The velocity of the particle of mass
Explanation of Solution
The expression for the relative velocity is,
Substitute
The overall elastic collision is described by the conservation of the momentum.
Substitute
Substitute
Conclusion:
Therefore, the velocity of the particle of mass
(d)
The velocity of the particle of mass
Answer to Problem 25.56AP
The velocity of the particle of mass
Explanation of Solution
From part (c) the value of
From part (c) the expression for
Substitute
Conclusion:
Therefore, the velocity of the particle of mass
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Chapter 25 Solutions
Physics for Scientists and Engineers, Volume 1
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