Concept explainers
(a)
Draw a sketch for the problem.
(a)
Answer to Problem 40PQ
Sketch for the problem,
Explanation of Solution
In the problem, the particle attached to the vertical spring is pulled down and released.
Sketch for the problem,
(b)
Draw the position-time graph.
(b)
Answer to Problem 40PQ
The position-time graph,
Explanation of Solution
Write the expression for position of the particle.
Here,
The position-time graph,
(c)
Draw the velocity-time graph.
(c)
Answer to Problem 40PQ
The velocity-time graph,
Explanation of Solution
Write the expression for position of the particle.
Here,
Derivate the position of the particle to find the velocity of the particle
Conclusion:
Substitute
The velocity-time graph,
(d)
Draw the acceleration-time graph.
(d)
Answer to Problem 40PQ
The acceleration -time graph,
Explanation of Solution
Write the expression for velocity of the particle.
Here,
Derivate the velocity of the particle to find the acceleration of the particle
Conclusion:
Substitute
The acceleration-time graph,
(e)
The time at which the speed of the particle is maximum and the position of the particle at maximum speed.
(e)
Answer to Problem 40PQ
The time at which the speed of the particle is maximum is
The particle will be at equilibrium position when it is at maximum speed.
Explanation of Solution
Write the expression for velocity of the particle.
Here,
Conclusion:
The speed of the particle is maximum if
(f)
The time at which the magnitude of acceleration of the particle is maximum and the position of the particle at maximum acceleration.
(f)
Answer to Problem 40PQ
The time at which the acceleration of the particle is maximum is
The particle will be at furthest away from equilibrium position when it is at maximum speed.
Explanation of Solution
Write the expression for velocity of the particle.
Here,
Conclusion:
The acceleration of the particle is maximum if
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Chapter 2 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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