Concept explainers
(a)
The x -component of the force as a function of x.
(a)
Explanation of Solution
Given:
The mass of the block is
Formula used:
Write the expression for the force exerted by a spring to a particle.
Here,
Calculation:
Write the expression for the force exerted on the block by the spring.
Here,
Write the expression for
Here,
Write the expression for
Substitute
Substitute
Write the expression for the
Substitute
Substitute
Conclusion:
Thus, the x-component of the force is
(b)
Whether the
(b)
Explanation of Solution
Calculation:
Rearrange the expression (5).
Expand the above expression in Taylor’s series and approximate up to second-order term.
Conclusion:
Thus, the
(c)
The speed of the block.
(c)
Explanation of Solution
Given:
The block is released from rest at
Formula Used:
Write the expression for the relation between final velocity, initial velocity, acceleration and the displacement of a particle.
Here,
Calculation:
Write the expression for the acceleration of the particle.
Substitute
Write the expression for the velocity of the particle when it crosses
Substitute
Conclusion:
Thus, the speed of the block is
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Chapter 6 Solutions
Physics for Scientists and Engineers
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